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 inf = 1061109567;
const long long infll = 4557430888798830399;
const int N = 405, MAX = 400;
int n, mod, ans[N], dp[N][N], fac[N], f[N];
void add(int &x, int y) {
  x += y;
  if (x >= mod) x -= mod;
}
int mul(int x, int y) { return 1ll * x * y % mod; }
void rem(int &x, int y) {
  x -= y;
  if (x < 0) x += mod;
}
void proc() {
  cin >> n;
  cout << ans[n] << "\n";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t >> mod;
  fac[0] = 1;
  for (int i = 1; i < N; i++) fac[i] = mul(fac[i - 1], i);
  dp[0][0] = 1;
  for (int i = 0; i < MAX; i++)
    for (int j = 0; j < i + 1; j++)
      if (dp[i][j]) {
        for (int k = 1; k < MAX - i + 1; k++)
          add(dp[i + k][j + 1], mul(dp[i][j], fac[k]));
      }
  for (int i = 1; i < MAX + 1; i++) {
    ans[i] = fac[i];
    for (int j = 3; j < i; j++) rem(ans[i], mul(dp[i][j], ans[j]));
    int lol = 0;
    for (int j = 1; j < i; j++) {
      int tmp1 = fac[j], tmp2 = fac[i - j];
      rem(tmp1, f[j]);
      add(lol, mul(tmp1, tmp2));
    }
    f[i] = lol;
    rem(ans[i], mul(lol, 2));
  }
  ans[2] = 2;
  while (t--) proc();
  return 0;
}