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 mod, fac[510], g[510], f[510], dp[510][510];
int main() {
  int T, n;
  scanf("%d%d", &T, &mod);
  fac[0] = 1;
  for (int i = 1; i <= 400; ++i) fac[i] = 1ll * fac[i - 1] * i % mod;
  for (int i = 1; i <= 400; ++i) {
    g[i] = fac[i];
    for (int j = 1; j < i; ++j) g[i] = (g[i] - 1ll * g[j] * fac[i - j]) % mod;
    g[i] = (g[i] + mod) % mod;
  }
  dp[0][0] = 1;
  for (int i = 0; i <= 400; ++i)
    for (int j = 0; j <= i; ++j) {
      int x = dp[i][j];
      if (!x) continue;
      for (int k = 1; i + k <= 400; ++k)
        dp[i + k][j + 1] = (dp[i + k][j + 1] + 1ll * x * fac[k]) % mod;
    }
  f[1] = 1;
  f[2] = 2;
  for (int i = 3; i <= 400; ++i) {
    f[i] = fac[i];
    for (int j = 1; j < i; ++j) f[i] = (f[i] - 2ll * g[j] * fac[i - j]) % mod;
    for (int j = 3; j < i; ++j) f[i] = (f[i] - 1ll * dp[i][j] * f[j]) % mod;
    f[i] = (f[i] + mod) % mod;
  }
  while (T--) {
    scanf("%d", &n);
    printf("%d\n", f[n]);
  }
  return 0;
}