Problem: Consider a permutation p_1, p_2, ... p_n of integers from 1 to n. We call a sub-segment p_l, p_{l+1}, ..., p_{r-1}, p_{r} of the permutation an interval if it is a reordering of some set of consecutive integers. For example, the permutation (6,7,1,8,5,3,2,4) has the intervals (6,7), (5,3,2,4), (3,2), and others. 

Each permutation has some trivial intervals — the full permutation itself and every single element. We call a permutation interval-free if it does not have non-trivial intervals. In other words, interval-free permutation does not have intervals of length between 2 and n - 1 inclusive. 

Your task is to count the number of interval-free permutations of length n modulo prime number p. 

Input

In the first line of the input there are two integers t (1 ≤ t ≤ 400) and p (10^8 ≤ p ≤ 10^9) — the number of test cases to solve and the prime modulo. In each of the next t lines there is one integer n (1 ≤ n ≤ 400) — the length of the permutation. 

Output

For each of t test cases print a single integer — the number of interval-free permutations modulo p. 

Examples

Input


4 998244353
1
4
5
9


Output


1
2
6
28146


Input


1 437122297
20


Output


67777575

Note

For n = 1 the only permutation is interval-free. For n = 4 two interval-free permutations are (2,4,1,3) and (3,1,4,2). For n = 5 — (2,4,1,5,3), (2,5,3,1,4), (3,1,5,2,4), (3,5,1,4,2), (4,1,3,5,2), and (4,2,5,1,3). We will not list all 28146 for n = 9, but for example (4,7,9,5,1,8,2,6,3), (2,4,6,1,9,7,3,8,5), (3,6,9,4,1,5,8,2,7), and (8,4,9,1,3,6,2,7,5) are interval-free.

The exact value for n = 20 is 264111424634864638. 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int TC;
long long MOD, f[401], fc[401], fi[401], g[401][401], O[401], h[401];
int main() {
  scanf("%d%lld", &TC, &MOD);
  fc[0] = fi[0] = fi[1] = 1;
  for (int i = 2; i <= 400; i++) fi[i] = (MOD - MOD / i) * fi[MOD % i] % MOD;
  for (int i = 1; i <= 400; i++) {
    fc[i] = fc[i - 1] * i % MOD;
    fi[i] = fi[i - 1] * fi[i] % MOD;
  }
  g[0][0] = 1;
  for (int i = 1; i <= 400; i++)
    for (int j = i; j <= 400; j++)
      for (int k = 1; k <= j - i + 1; k++)
        g[i][j] = (g[i][j] + g[i - 1][j - k] * fc[k]) % MOD;
  for (int i = 1; i <= 400; i++) {
    f[i] = fc[i];
    for (int j = 1; j <= i - 2; j++)
      f[i] = (f[i] - g[j][i - 1] * f[j + 1] % MOD + MOD) % MOD;
  }
  for (int i = 1; i <= 400; i++) {
    O[i] = f[i];
    for (int j = 2; j < i; j++)
      O[i] = (O[i] - O[i - j + 1] * f[j] % MOD + MOD) % MOD;
  }
  while (TC--) {
    int n;
    scanf("%d", &n);
    if (n <= 2)
      printf("%lld\n", O[n]);
    else if (n & 1)
      printf("%lld\n", (O[n] + 2) % MOD);
    else
      printf("%lld\n", (O[n] - 2 + MOD) % MOD);
  }
  return 0;
}