For set \(A\), let \[v(A) = \sum_{S \subset A, |S| \equiv 1 \pmod 2}(\prod_{x \in S}x)\]
Initially, \(A\) is empty. Your task is to insert and delete element keeping track of value of \(v(A)\).
The first line contains the only integer \(q\), which denotes the number of operations.
The following \(q\) lines, which is either "insert \(x\)" or "delete \(x\)".
For convinience, one can assume that \(A\) is a multiset and there are no delete operations for non-exist elements.
\((1 \leq q \leq 10^5, 2 \leq x \leq 10^9)\)
After each operation, print a single integer showing \(v(A) \bmod (10^9 + 7)\).
4
insert 2
insert 3
insert 4
delete 3
2
5
33
6
After \(4\) is inserted, \(A = \{2, 3, 4\}\). Thus, \(v(A) = 2 + 3 + 4 + 2 \cdot 3 \cdot 4 = 33\).