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>
using namespace std;
const int N = 400;
int main() {
  int tt, md;
  scanf("%d %d", &tt, &md);
  auto add = [&](int &x, int y) {
    x += y;
    if (x >= md) {
      x -= md;
    }
  };
  auto sub = [&](int &x, int y) {
    x -= y;
    if (x < 0) {
      x += md;
    }
  };
  auto mul = [&](int x, int y) { return (long long)x * y % md; };
  vector<int> fact(N + 1);
  fact[0] = 1;
  for (int i = 0; i < N; ++i) {
    fact[i + 1] = mul(fact[i], i + 1);
  }
  vector<int> ways(N + 1);
  for (int i = 1; i <= N; ++i) {
    ways[i] = fact[i];
    for (int j = 1; j < i; ++j) {
      sub(ways[i], mul(ways[j], fact[i - j]));
    }
  }
  vector<vector<int>> dp(N + 1, vector<int>(N + 1));
  dp[0][0] = 1;
  for (int i = 1; i <= N; ++i) {
    for (int j = 1; j <= i; ++j) {
      for (int k = 1; k <= i; ++k) {
        add(dp[i][j], mul(dp[i - k][j - 1], fact[k]));
      }
    }
  }
  vector<int> f(N + 1);
  for (int i = 1; i <= N; ++i) {
    f[i] = fact[i];
    for (int j = 1; j < i; ++j) {
      sub(f[i], mul(2, mul(ways[j], fact[i - j])));
    }
    for (int j = 3; j < i; ++j) {
      sub(f[i], mul(dp[i][j], f[j]));
    }
  }
  f[2] = 2;
  while (tt--) {
    int n;
    scanf("%d", &n);
    printf("%d\n", f[n]);
  }
  return 0;
}