시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
3 초 (추가 시간 없음) | 1024 MB | 1 | 1 | 1 | 100.000% |
Do you know this problem: https://atcoder.jp/contests/agc022/tasks/agc022_e? We generalize it a bit.
You got a binary string $P = P_0P_1P_2P_3P_4P_5P_6P_7$ of length $8$.
You think a binary string $X$ of odd length $N$ is beautiful if it is possible to apply the following operation $\frac{N-1}{2}$ times so that the only character of the resulting string is '1
' :
Note that, when $P = 00010111$, this definition is the same as the original AGC problem.
You have a string $S$ consisting of characters '0
', '1
', and '?
'. You want to know the number of ways to replace the question marks with '1
' or '0
' so that the resulting string is beautiful, modulo $10^9 + 7$.
Note that there are $T$ tests in one input file.
Input is given from Standard Input in the following format:
$T$
$P$ $S$
$P$ $S$
$\vdots$
$P$ $S$
For each case, print the answer in a line.
7 00010111 1??00 00010111 ? 00010111 ?0101???10???00?1???????????????0????????????1????0 01010101 1???? 01010101 0???? 00001111 1???? 00001111 0????
2 1 402589311 16 0 8 8