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;
long long F[444][444], Ans[444], Fac[444], O[444], n, P;
int MxN = 400;
void add(long long &x, long long y) { x = (x + y) % P; }
int main() {
  scanf("%lld%lld", &n, &P);
  for (int i = 0; i <= MxN; i++) Fac[i] = !i ? 1 : Fac[i - 1] * i % P;
  Ans[1] = 1;
  Ans[2] = 2;
  F[0][0] = 1;
  F[1][1] = 1;
  F[2][1] = 2;
  F[2][2] = 1;
  O[1] = 1;
  O[2] = 1;
  for (int i = 3; i <= MxN; i++) {
    O[i] = Fac[i];
    for (int j = 1; j < i; j++) add(O[i], -O[j] * Fac[i - j]);
  }
  for (int i = 3; i <= MxN; i++) {
    for (int j = 1; j <= i; j++)
      for (int k = 1; k <= i; k++) add(F[i][j], F[i - k][j - 1] * Fac[k]);
    long long tot = Fac[i];
    for (int j = 3; j < i; j++) add(tot, -F[i][j] * Ans[j]);
    for (int j = 1; j < i; j++) add(tot, -2ll * Fac[j] % P * O[i - j]);
    Ans[i] = tot;
  }
  while (n--) {
    int x;
    scanf("%d", &x);
    printf("%lld\n", (Ans[x] % P + P) % P);
  }
  return 0;
}