… \u5927\u5bb6\u597d\u6211\u662f Lucas \u5b9a\u7406 .. .<\/p>\n
<\/p>\n
http:\/\/en.wikipedia.org\/wiki\/Lucas%27_theorem<\/p>\n
… \u53ef\u4ee5\u7528\u6211\u6765\u6c42 mod p \u7ec4\u5408\u6570..
\n\u3002\u3002\u672c\u6a21\u677f p \u8981\u63a7\u5236\u5728 10000 \u4ee5\u5185\u3002
\n\u3002\u3002\u5bf9\u4e8e\u6c42\u9636\u4e58\u9006\u5143\uff0c\u4f3c\u4e4e\u6709\u7a0d\u5fae\u5feb\u4e00\u4e9b\u7684\u65b9\u6cd5\u3002<\/p>\n
\r\n\/** ` Micro Mezzo Macro Flation -- Overheated Economy ., **\/\r\n\r\n#include <algorithm>\r\n#include <iostream>\r\n#include <iomanip>\r\n#include <sstream>\r\n#include <cstring>\r\n#include <cstdio>\r\n#include <string>\r\n#include <vector>\r\n#include <bitset>\r\n#include <queue>\r\n#include <cmath>\r\n#include <ctime>\r\n#include <list>\r\n#include <set>\r\n#include <map>\r\n\r\nusing namespace std;\r\n\r\n#define REP(i, n) for (int i=0;i<int(n);++i)\r\n#define FOR(i, a, b) for (int i=int(a);i<int(b);++i)\r\n#define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)\r\n#define REP_1(i, n) for (int i=1;i<=int(n);++i)\r\n#define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)\r\n#define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)\r\n#define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)\r\n#define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)\r\n#define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)\r\n#define REP_N(i, n) for (i=0;i<int(n);++i)\r\n#define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)\r\n#define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)\r\n#define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)\r\n#define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)\r\n#define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)\r\n#define REP_1_N(i, n) for (i=1;i<=int(n);++i)\r\n#define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)\r\n#define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)\r\n#define REP_C_N(i, n) for (n____=int(n),i=0;i<n____;++i)\r\n#define FOR_C_N(i, a, b) for (b____=int(b),i=a;i<b____;++i)\r\n#define DWN_C_N(i, b, a) for (a____=int(a),i=b-1;i>=a____;--i)\r\n#define REP_1_C_N(i, n) for (n____=int(n),i=1;i<=n____;++i)\r\n#define FOR_1_C_N(i, a, b) for (b____=int(b),i=a;i<=b____;++i)\r\n#define DWN_1_C_N(i, b, a) for (a____=int(a),i=b;i>=a____;--i)\r\n\r\n#define DO(n) while(n--)\r\n#define DO_C(n) int n____ = n; while(n____--)\r\n#define TO(i, a, b) int s_=a<b?1:-1,b_=b+s_;for(int i=a;i!=b_;i+=s_)\r\n#define TO_1(i, a, b) int s_=a<b?1:-1,b_=b;for(int i=a;i!=b_;i+=s_)\r\n#define SQZ(i, j, a, b) for (int i=int(a),j=int(b)-1;i<j;++i,--j)\r\n#define SQZ_1(i, j, a, b) for (int i=int(a),j=int(b);i<=j;++i,--j)\r\n#define REP_2(i, j, n, m) REP(i, n) REP(j, m)\r\n#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)\r\n\r\n#define ALL(A) A.begin(), A.end()\r\n#define LLA(A) A.rbegin(), A.rend()\r\n#define CPY(A, B) memcpy(A, B, sizeof(A))\r\n#define INS(A, P, B) A.insert(A.begin() + P, B)\r\n#define ERS(A, P) A.erase(A.begin() + P)\r\n#define BSC(A, X) find(ALL(A), X) \/\/ != A.end()\r\n#define CTN(T, x) (T.find(x) != T.end())\r\n#define SZ(A) int(A.size())\r\n#define PB push_back\r\n#define MP(A, B) make_pair(A, B)\r\n\r\n#define Rush int T____; RD(T____); DO(T____)\r\n#pragma comment(linker, "\/STACK:36777216")\r\n#pragma GCC optimize ("O2")\r\n#define Ruby system("ruby main.rb")\r\n#define Haskell system("runghc main.hs")\r\n#define Pascal system("fpc main.pas")\r\n\r\ntypedef long long LL;\r\ntypedef double DB;\r\ntypedef unsigned UINT;\r\ntypedef unsigned long long ULL;\r\n\r\ntypedef vector<int> VI;\r\ntypedef vector<char> VC;\r\ntypedef vector<string> VS;\r\ntypedef vector<LL> VL;\r\ntypedef vector<DB> VD;\r\ntypedef set<int> SI;\r\ntypedef set<string> SS;\r\ntypedef set<LL> SL;\r\ntypedef set<DB> SD;\r\ntypedef map<int, int> MII;\r\ntypedef map<string, int> MSI;\r\ntypedef map<LL, int> MLI;\r\ntypedef map<DB, int> MDI;\r\ntypedef map<int, bool> MIB;\r\ntypedef map<string, bool> MSB;\r\ntypedef map<LL, bool> MLB;\r\ntypedef map<DB, bool> MDB;\r\ntypedef pair<int, int> PII;\r\ntypedef pair<int, bool> PIB;\r\ntypedef vector<PII> VII;\r\ntypedef vector<VI> VVI;\r\ntypedef vector<VII> VVII;\r\ntypedef set<PII> SII;\r\ntypedef map<PII, int> MPIII;\r\ntypedef map<PII, bool> MPIIB;\r\n\r\n\r\n\/** I\/O Accelerator **\/\r\n\r\n\/* ... :" We are I\/O Accelerator ... Use us at your own risk ;) ... " .. *\/\r\n\r\ntemplate<class T> inline void RD(T &);\r\ntemplate<class T> inline void OT(const T &);\r\n\r\ninline int RD(){ int x; RD(x); return x;}\r\ntemplate<class T> inline T& _RD(T &x){ RD(x); return x;}\r\ninline void RC(char &c){scanf(" %c", &c);}\r\ninline void RS(char *s){scanf("%s", s);}\r\n\r\ntemplate<class T0, class T1> inline void RD(T0 &x0, T1 &x1){RD(x0), RD(x1);}\r\ntemplate<class T0, class T1, class T2> inline void RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void 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);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void 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);}\r\ntemplate<class T0, class T1> inline void OT(T0 &x0, T1 &x1){OT(x0), OT(x1);}\r\ntemplate<class T0, class T1, class T2> inline void OT(T0 &x0, T1 &x1, T2 &x2){OT(x0), OT(x1), OT(x2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}\r\n\r\ntemplate<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}\r\ntemplate<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}\r\ntemplate<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<class T> inline void CLR(T &A){A.clear();}\r\ntemplate<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}\r\ntemplate<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<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);}\r\ntemplate<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}\r\ntemplate<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}\r\ntemplate<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}\r\ntemplate<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2){FLC(A0), FLC(A1), FLC(A2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3){FLC(A0), FLC(A1), FLC(A2), FLC(A3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);}\r\ntemplate<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){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);}\r\ntemplate<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){FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);}\r\n\r\ntemplate<class T> inline void SRT(T &A){sort(ALL(A));}\r\ntemplate<class T, class C> inline void SRT(T &A, C B){sort(ALL(A), B);}\r\n\r\n\r\n\/** Add - On **\/\r\n\r\nint MOD = 1000000007;\r\nconst int INF = 0x7fffffff;\r\nconst DB PI = acos(-1.0);\r\nconst DB EPS = 1e-6;\r\nconst DB OO = 1e15;\r\n\r\n\/\/ <<= ` 0. Daily Use .,\r\n\r\ntemplate<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}\r\ntemplate<class T> inline void checkMax(T &a,const T b){if (b>a) a=b;}\r\ntemplate <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}\r\ntemplate <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}\r\ntemplate<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}\r\ntemplate<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}\r\ntemplate<class T> inline T sqr(T a){return a*a;}\r\ntemplate<class T> inline T cub(T a){return a*a*a;}\r\nint Ceil(int x, int y){return (x - 1) \/ y + 1;}\r\n\r\n\/\/ <<= ` 1. Bitwise Operation .,\r\n\r\ninline bool _1(int x, int i){return x & 1<<i;}\r\ninline int _1(int i){return 1<<i;}\r\ninline int _U(int i){return _1(i) - 1;};\r\n\r\ninline int count_bits(int x){\r\n x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);\r\n x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);\r\n x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);\r\n x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);\r\n x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);\r\n return x;\r\n}\r\n\r\ntemplate<class T> inline T low_bit(T x) {\r\n return x & -x;\r\n}\r\n\r\ntemplate<class T> inline T high_bit(T x) {\r\n T p = low_bit(x);\r\n while (p != x) x -= p, p = low_bit(x);\r\n return p;\r\n}\r\n\r\n\/\/ <<= ` 2. Modular Arithmetic Basic .,\r\n\r\ninline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}\r\ninline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}\r\ninline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}\r\ninline int dff(int a, int b){a -= b; if (a < 0) a += MOD; return a;}\r\ninline void MUL(int &a, int b){a = a * b % MOD;}\r\ninline int pdt(int a, int b){return a * b % MOD;}\r\n\r\n\r\ninline int pow(int a, int b){\r\n int c = 1;\r\n while (b) {\r\n if (b&1) MUL(c, a);\r\n MUL(a, a), b >>= 1;\r\n }\r\n return c;\r\n}\r\n\r\ninline int _I(int b){\r\n\tint a = MOD, x1 = 0, x2 = 1, q;\r\n\twhile (true){\r\n\t\tq = a \/ b, a %= b;\r\n\t\tif (!a) return (x2 + MOD) % MOD;\r\n\t\tDEC(x1, pdt(q, x2));\r\n\r\n\t\tq = b \/ a, b %= a;\r\n\t\tif (!b) return (x1 + MOD) % MOD;\r\n\t\tDEC(x2, pdt(q, x1));\r\n\t}\r\n}\r\n\r\ninline void DIV(int &a, int b){MUL(a, _I(b));}\r\ninline int qtt(int a, int b){return pdt(a, _I(b));}\r\n\r\n\r\n\/\/ <<= ' 0. I\/O Accelerator interface .,\r\n\r\ntemplate<class T> inline void RD(T &x){\r\n \/\/cin >> x;\r\n \/\/scanf("%d", &x);\r\n char c; for (c = getchar(); c < '0'; c = getchar()); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';\r\n \/\/char c; c = getchar(); x = c - '0'; for (c = getchar(); c >= '0'; c = getchar()) x = x * 10 + c - '0';\r\n\r\n}\r\n\r\n\/\/int ____Case;\r\ntemplate<class T> inline void OT(const T &x){\r\n \/\/cout << x << endl;\r\n printf("%d\\n", x);\r\n \/\/printf("%.2lf\\n", x);\r\n \/\/printf("Case %d: %d\\n", ++____Case, x);\r\n}\r\n\r\n\r\n#define For_each(it, A) for (SII::iterator it = A.begin(); it != A.end(); ++it)\r\n\r\n\/* .................................................................................................................................. *\/\r\n\r\nconst int N = 9973, M = 1229, L = 1001;\r\n\r\nint P[M], F[M][N], F_[M][N];\r\nint n, m;\r\n\r\nint h(int p){\r\n return lower_bound(P, P + M, p) - P;\r\n}\r\n\r\nvoid init(){\r\n\r\n bitset<N> C;\r\n\r\n FOR_1(i, 2, N){\r\n\r\n if(!C[i]) P[m++] = i;\r\n\r\n REP_C(j, m){\r\n if (i * P[j] >= N) break;\r\n C[i * P[j]] = true;\r\n }\r\n }\r\n\r\n\/*\r\n REP(i, m){\r\n F[i][0] = F[i][1] = F_[i][0] = F_[i][1] = 1;\r\n FOR_C(j, 2, MOD = P[i]){\r\n F[i][j] = pdt(F[i][j-1], j);\r\n _F[i][j] = qtt(_F[i][j-1], j);\r\n }\r\n }\r\n*\/\r\n\r\n REP(i, m){\r\n F[i][0] = F[i][1] = F_[i][0] = F_[i][1] = 1;\r\n FOR_C(j, 2, MOD = P[i]){\r\n F[i][j] = pdt(F[i][j-1], j);\r\n F_[i][j] = -MOD \/ j * F_[i][MOD % j] % MOD;\r\n if (F_[i][j] < 0) F_[i][j] += MOD;\r\n }\r\n }\r\n\r\n REP(i, m) FOR(j, 2, MOD = P[i])\r\n MUL(F_[i][j], F_[i][j-1]);\r\n}\r\n\r\n\r\nint _c(int n, int m){\r\n\r\n if (n < m) return 0; int p = h(MOD);\r\n return pdt(pdt(F[p][n], F_[p][m]), F_[p][n-m]);\r\n}\r\n\r\nint c(int n, int m){\r\n int res = 1;\r\n while (n && m){\r\n MUL(res, _c(n % MOD, m % MOD));\r\n n \/= MOD, m \/= MOD;\r\n }\r\n return res;\r\n}\r\n\r\n\r\nint main(){\r\n\r\n init();\r\n\r\n while (cin >> n >> m >> MOD){\r\n OT(c(n, m));\r\n }\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Brief description : … \u5927\u5bb6\u597d\u6211\u662f Lucas \u5b9a\u7406 .. .<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[38],"class_list":["post-50","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-38"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-O","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=50"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/50\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=50"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=50"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}