某島

… : "…アッカリ~ン . .. . " .. .
April 20, 2020

SPOJ CAKE3. Delicious Cake

Vjudge | SPOJ
https://t.me/algorithm_daily_of_minako/149

先複習一下插頭 dp 大字典。本題顯然使用染色模型。輪廓線上只有 m 個位置,而且不需要 roll() 操作(不過生成的新插頭,要求前面的區分開來,所以我們還是用 m+1 來標記)。

這樣搞得話,2×2 我們會算出答案等於 14,仔細觀察,是因為我們多算了下面兩種不合法的情況。

我們發現這類情況都是因為在前面的轉移中產生了刻痕,而使得後續的插頭合併不合法,需要進一步編碼。
我們可以給每個連通塊強行上一個顏色,不相同的顏色不可合併。但是因為原問題沒有顏色,這樣計數起來會比較麻煩(需要最小染色,並且必須保證相同顏色的連通塊必被合併)。
我們也可以暴力記錄 C(5,2) 個連通塊之間是否產生過刻痕,這樣合併的時候直接判斷即可。

刻痕的維護,首先每次狀態轉移,當前插頭都需要和相鄰兩個插頭(左插頭和上插頭)都標記刻痕。
其次,因為我們使用了最小表示,連通塊的記號會被 relable,因而編碼的時候也需要重新映射。
最後插頭合併的時候,刻痕信息也需要合併。

最後上一下高精度模板就好了。留個 OEIS 地址方便大家 debug

/*
    This code has been written by MinakoKojima, feel free to ask me question. Blog: http://www.shuizilong.com/house
    Template Date: 2015.10.12
    Note: ...
*/

#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>

//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>

using namespace std;

#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)

#define ECH(it, A) for (__typeof((A).begin()) it=(A).begin(); it != (A).end(); ++it)
#define rECH(it, A) for (__typeof((A).rbegin()) it=(A).rbegin(); it != (A).rend(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)

#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (upper_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()

#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) {                      \
  REP(i, n){		                            \
        REP(j, m-1) cout << A[i][j] << " ";     \
        cout << A[i][m-1] << endl;		        \
	}						                    \
}
#define Display_1(A, n, m) {                    \
	REP_1(i, n){		                        \
        REP_1(j, m-1) cout << A[i][j] << " ";   \
        cout << A[i][m] << endl;		        \
	}						                    \
}

typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;

typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;

template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}

template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}

template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline T0& RDD(T0&a, T1&b){RDD(a),RDD(b); return a;}
template<class T0,class T1,class T2>inline T1& RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c); return a;}

template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}

template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T> &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T> inline void CLR(queue<T> &Q){while (!Q.empty()) Q.pop();}

template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}

template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C cmp){sort(ALL(A), cmp); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
template<class T, class C> inline T& UNQ(T &A, C cmp){SRT(A, cmp);return UNQQ(A);}


//}

/** Constant List .. **/ //{

const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;

const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, 1, -1};

//}

/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{

template<class T> inline bool checkMin(T &a,const T b){return b < a ? a = b, 1 : 0;}
template<class T> inline bool checkMax(T &a,const T b){return a < b ? a = b, 1 : 0;}
template <class T, class C> inline bool checkUpd(T& a, const T b, C c){return c(b,a) ? a = b, 1 : 0;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}

inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};

//}

//}



/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
    char c;while(!d);x=c-'0';while(d)p;
    return x;
}
template<class T> inline T& RDD(T &x){
    char c;while(g,c!='-'&&!isdigit(c));
    if (c=='-'){x='0'-g;while(d)n;}
    else{x=c-'0';while(d)p;}
    return x;
}
inline DB& RF(DB &x){
    //scanf("%lf", &x);
    char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
    if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
        else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
    else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
        else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
    return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
    //gets(s);
    scanf("%s", s);
    return s;
}

LL last_ans; int Case; template<class T> inline void OT(const T &x){
    //printf("Case #%d: ", ++Case);
    //printf("%lld\n", x);
    //printf("%I64d\n", x);
    //printf("%.9f\n", x);
    //printf("%d\n", x);
    cout << x << endl;
    //last_ans = x;
}


//}/* .................................................................................................................................. */


// <<= 'Bignum ., //{
namespace BIGNUM{

const int __base = 1e8;
const int P10[] = {1, 10, int(1e2), int(1e3), int(1e4), int(1e5), int(1e6), int(1e7), int(1e8), int(1e9)};
const int MAX_BUF_SIZE = 109;
char __buf[MAX_BUF_SIZE];

class bignum{
          friend istream& operator>>(istream&, bignum&);
          friend ostream& operator<<(ostream&, const bignum&);
          friend bignum operator +(const bignum&, const bignum&);
          friend bignum operator +(const bignum&, const int&);
          friend bool operator ==(const bignum&, const bignum&);
          friend bool operator !=(const bignum&, const bignum&);
          friend bool operator <(const bignum&, const bignum&);
          friend bool operator >(const bignum&, const bignum&);
          friend bool operator <=(const bignum&, const bignum&);
          friend bool operator >=(const bignum&, const bignum&);
          friend bool operator ==(const bignum&, const int&);
          friend bool operator !=(const bignum&, const int&);
          friend bool operator <(const bignum&, const int&);
          friend bool operator >(const bignum&, const int&);
          friend bool operator <=(const bignum&, const int&);
          friend bool operator >=(const bignum&, const int&);
          friend int do_comp(const bignum&, const int&);
          friend int do_comp(const bignum&, const bignum&);
          friend void divide(const bignum&, const bignum&, bignum&, bignum&);
          friend bignum pow(bignum, int);
          friend bignum pow(int, int);
    public:
        inline bignum(){};
        inline bignum(int s){
            while (s) data.PB(s%__base), s/=__base;
            if (data.empty()) data.PB(0);
        }

        inline bignum(long long s){
            while (s) data.PB(int(s%__base)), s/=__base;
            if (data.empty()) data.PB(0);
        }

        inline bignum(string s){
            int t, i; CLR(data);
            for (i=int(s.size())-8;i>0;i-=8){
                istringstream(s.substr(i, 8)) >> t;
                data.PB(t);
            }
            istringstream(s.substr(0, i+8)) >> t;
            data.PB(t);
        }

        void input(){
            CLR(data); RS(__buf); int t = 0, c = 0;
            DWN(i, strlen(__buf), 0){
                t += P10 * (int(__buf[i]) - '0'), ++c;
                if (c == 8) data.PB(t), c = t = 0;
            }
            if (c) data.PB(t);
        }

        bignum&operator=(int);
        bignum&operator=(const string&);
        bignum&operator=(const bignum&);
        bignum&operator +=(const bignum&);
        bignum&operator -=(const bignum&);
        bignum&operator *=(const bignum&);
        bignum&operator /=(const bignum&);
        bignum&operator %=(const bignum&);
        bignum&operator +=(const int&);
        bignum&operator -=(const int&);
        bignum&operator *=(const int&);
        bignum&operator /=(const int&);
        bignum&operator %=(const int&);
        bool undefined();
        int do_try(const int&);
        int do_try(const bignum&);
        void do_trim();
        list<int> data;

    int size(){
        list<int>::iterator it; int res = 0;
        for (it=data.begin(); it!=data.end();it++)
            res += 8;
        it--;
        if (*it >= 10000) {
            if ( (*it) >= 1000000) {if (*it >=10000000) ; else res--;}
            else {if ((*it) >= 100000) res-=2; else res-=3;}
        }
        else
            if ( (*it) >= 100) {if (*it >=1000) res-=4; else res-=5;}
            else {if ((*it) >= 10) res-=6; else res-=7;}

        return res;
    }

    void do_reserve(int a){
        if (a <= 0) return;
        list<int>::iterator it;
        for (it=data.begin(); it!=data.end() && a>0; it++) a-=8;
        if (it == data.end() && a>=0) return;
        a+=8, it--; int f = 1;
        for (int i=0;i<a;i++) f *= 10; (*it) %= f;
        data.erase(++it, data.end());
        do_trim();
    }
};

inline bignum&bignum::operator =(const bignum&a){
    data.clear();
    for (list<int>::const_iterator i=a.data.begin();i!=a.data.end();i++){
        data.PB(*i);
    }
    return*this;
}
inline bignum&bignum::operator =(const string&a){
    return*this=bignum(a);
}
inline bignum&bignum::operator =(int a){
    return*this=bignum(a);
}

inline istream& operator>>(istream& input, bignum& a){
    string s; int t, i; input >> s; a.data.clear();
    for (i=int(s.size())-8;i>0;i-=8){
        istringstream(s.substr(i, 8)) >> t;
        a.data.PB(t);
    }
    istringstream(s.substr(0, i+8)) >> t;
    a.data.PB(t);
    return input;
}

inline ostream& operator<<(ostream& output, const bignum& a){
    list<int>::const_reverse_iterator i=a.data.rbegin();
    output << *i;
    for (i++;i!=a.data.rend();i++){
        if (*i >= 10000) {
            if (*i >= 1000000) {if (*i>=10000000) cout << *i; else cout << 0 << *i;}
            else {if (*i>=100000) cout << "00" << *i; else cout << "000" << *i;}
        }
        else {
            if (*i >= 100) {if (*i>=1000)  cout << "0000" << *i; else cout << "00000" << *i;}
            else { if (*i>=10) cout << "000000" << *i; else cout << "0000000" << *i;}
        }
    }
    return output;
}

inline bool bignum::undefined(){
    return data.empty();
}

inline int do_comp(const bignum& a, const bignum& b){
    if (a.data.size()<b.data.size()) return -1; if (a.data.size()>b.data.size()) return 1;
    list<int>::const_reverse_iterator i; list<int>::const_reverse_iterator j;
    for (i=a.data.rbegin(),j=b.data.rbegin(); j!=b.data.rend(); i++,j++){
        if (*i<*j) return -1;              //!!!!
        if (*i>*j) return 1;
    }
    return 0;
}
inline int do_comp(const bignum& a, const int& b){
    return do_comp(a, bignum(b));
}

inline bool operator ==(const bignum& a, const bignum& b){
    return do_comp(a, b) == 0;
}
inline bool operator !=(const bignum& a, const bignum& b){
    return do_comp(a, b) != 0;
}
inline bool operator <(const bignum& a, const bignum& b){
    return do_comp(a, b) == -1;
}
inline bool operator >(const bignum& a, const bignum& b){
    return do_comp(a, b) == 1;
}
inline bool operator <=(const bignum& a, const bignum& b){
    return do_comp(a, b) != 1;
}
inline bool operator >=(const bignum& a, const bignum& b){
    return do_comp(a, b) != -1;
}

inline bool operator ==(const bignum& a, const int& b){
    return do_comp(a, b) == 0;
}
inline bool operator !=(const bignum& a, const int& b){
    return do_comp(a, b) != 0;
}
inline bool operator <(const bignum& a, const int& b){
    return do_comp(a, b) == -1;
}
inline bool operator >(const bignum& a, const int& b){
    return do_comp(a, b) == 1;
}
inline bool operator <=(const bignum& a, const int& b){
    return do_comp(a, b) != 1;
}
inline bool operator >=(const bignum& a, const int& b){
    return do_comp(a, b) != -1;
}

inline void bignum::do_trim(){
    while (data.size()>1&&data.back()==0) data.pop_back();
}

inline bignum& bignum::operator +=(const bignum& a){
    list<int>::iterator i; list<int>::const_iterator j; int t = 0;
    for (i=data.begin(),j=a.data.begin(); i!=data.end()&&j!=a.data.end(); i++,j++){
        *i+=*j+t; t=*i/__base; *i%=__base;
    }
    while (i!=data.end()) {*i+=t; t=*i/__base; *i%=__base; i++;}
    while (j!=a.data.end()) {data.PB(t+*j); t=data.back()/__base; data.back()%=__base; j++;}
    if (t!=0) data.PB(t);
    return *this;
}

inline bignum& bignum::operator +=(const int& a){
    return (*this)+=bignum(a);
}

inline bignum operator +(const bignum& a, const bignum& b){
    list<int>::const_iterator i, j; bignum c; int t = 0;
    for (i=a.data.begin(),j=b.data.begin(); i!=a.data.end()&&j!=b.data.end(); i++,j++){
        c.data.PB(t+*i+*j);
        t=c.data.back()/__base; c.data.back()%=__base;
    }
    while (i!=a.data.end()) {c.data.PB(t+*i); t=c.data.back()/__base; c.data.back()%=__base; i++;}
    while (j!=b.data.end()) {c.data.PB(t+*j); t=c.data.back()/__base; c.data.back()%=__base; j++;}
    if (t!=0) c.data.PB(t);
    return c;
}

inline bignum operator +(const bignum& a, const int& b){
    return a+bignum(b);
}

} using namespace BIGNUM;
//}

typedef int T_state;
typedef bignum T_key;
const int N = 8;
int n, m;

// 5*3 = 15
// 4321 = 10

const int Offset = 3, Mask = (1 << Offset) - 1;
bool ok[N][N], okk[N][N], _ok[N];

int b[N+2], bb[N+3];
T_state encode() {
    T_state s = 0; memset(bb, -1, sizeof(bb)); int bn = 1; bb[0] = 0;
#define bi bb[b[i]]
#define bj bb[b[j]]
    DWN(i, m, 0) {
        if (!~bi) bi = bn++;
    }

    memset(okk, 1, sizeof(okk));
    //cout << "b: "; FOR(i, 0, m) cout << b[i] << " "; cout << endl;
    REP(i, m) if (b[i]) {
        REP(j, i) if (b[j]) {
            okk[bi][bj] = okk[bj][bi] = ok[b[i]][b[j]];
        }
    }
    DWN(i, m+1, 2) DWN(j, i, 1) {
        s <<= 1; s |= !okk[i][j];
    }
    DWN(i, m, 0) {
        s <<= Offset; s |= bi;
    }
    return s;
}
void decode(T_state s){
    REP(i, m) {
        b[i] = s & Mask;
        s >>= Offset;
    }
    memset(ok, 1, sizeof(ok));
    FOR(i, 2, m+1) FOR(j, 1, i) {
        ok[i][j] = ok[j][i] = !(s&1);
        s >>= 1;
    }
}
const int Prime = 9979, MaxSZ = 1 << 20;
T_key d;
template<class T_state, class T_key> struct hashTable {
    int head[Prime]; int next[MaxSZ], sz;
    T_state state[MaxSZ]; T_key key[MaxSZ];
    void clear() {
        sz = 0;
        memset(head, -1, sizeof(head));
    }
    void push(T_state s) {
        int x = s % Prime;
        for (int i = head[x]; ~i; i = next[i]) {
            if (state[i] == s) {
                key[i] += d;
                return;
            }
        }
        state[sz] = s, key[sz] = d;
        next[sz] = head[x], head[x] = sz++;
    }
};
hashTable<T_state, T_key> H[2], *H0, *H1;

//
// 64 // 32 16 8 // . . .

int j, lf, up;
void push(int t) {
    b[j] = t;
    //assert(ok[t][lf] == ok[lf][t]);
    //assert(ok[t][up] == ok[up][t]);
    bool ok_lf = ok[t][lf], ok_up = ok[t][up];
    ok[t][lf] = ok[lf][t] = ok[t][up] = ok[up][t] = 0;
    H1->push(encode());
    ok[t][lf] = ok[lf][t] = ok_lf;
    ok[t][up] = ok[up][t] = ok_up;
}
void push() {
    H1->push(encode());
}

void init() {
    cin >> n >> m; if (m > n) swap(n, m);
}
void solve() {
    H0 = H, H1 = H+1, H1->clear(), d = 1, H1->push(0);

    REP(i, n) {
        REP(j, m) {
            ::j = j; swap(H0, H1), H1->clear();
            REP(u, H0->sz) {
                decode(H0->state[u]); d = H0->key[u];
                lf = j ? b[j-1] : 0, up = b[j];

                /*cout << H0->state[u] << ": " << d << endl;
                REP(i, m) cout << b[i] << " "; cout << endl;
                cout << "c: "; FOR(i, 1, m+1) FOR(j, 1, i) cout << ok[i][j] << " "; cout << endl;
*/

                push(m+1);
                if (lf && up) {
                    push(lf);
                    if (lf!=up) {
                        push(up);
                        if (ok[lf][up]) {
                            //if (lf > up) swap(lf, up);
                            REP(i, m) if (b[i] == up) b[i] = lf;
                            FOR(t, 1, m+1) {
                                _ok[t] = ok[lf][t];
                                if (ok[lf][t] && !ok[up][t]) {
                                    ok[lf][t] = ok[t][lf] = 0;
                                }
                            }
                            push();
                            FOR(t, 1, m+1) ok[lf][t] = ok[t][lf] = _ok[t];
                        }
                    }
                } else if (lf | up) {
                    push(lf|up);
                }
            }
        }
        //H1->roll();
    }

    /*H0 = H1;
    REP(u, H0->sz) {
        decode(H0->state[u]); d = H0->key[u];
        cout << H0->state[u] << ": " << d << endl;
        REP(i, m) cout << b[i] << " "; cout << endl;
    }*/
}
void print() {
    T_key z = 0; REP(i, H1->sz) z += H1->key[i];
    cout << z << endl;
}
int main(){
#ifndef ONLINE_JUDGE
    ////freopen("in.txt", "r", stdin);
#endif
    int T; cin >> T; while (T--) {
        init(); solve();
        print();
    }
}

// 不考慮切痕迹