Count the number of n x n matrices A satisfying the following condition modulo m.
* Ai, j ∈ {0, 1, 2} for all 1 ≤ i, j ≤ n.
* Ai, j = Aj, i for all 1 ≤ i, j ≤ n.
* Ai, 1 + Ai, 2 + ... + Ai, n = 2 for all 1 ≤ i ≤ n.
* A1, 1 = A2, 2 = ... = An, n = 0.
输入描述：
The input consists of several test cases and is terminated by end-of-file. Each test case contains two integers n and m.
输出描述：
For each test case, print an integer which denotes the result.
备注 * 1 ≤ n ≤ 10 5 * 1 ≤ m ≤ 10 9 * The sum of n does not exceed 10 7 .
示例1:
输入
3 1000000000
100000 1000000000
输出
1
507109376