Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.

He wrote an integer X on the blackboard, then performed the following operation N times:

* Choose one element from S and remove it.
* Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.



There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.

Constraints

* All values in input are integers.
* 1 \leq N \leq 200
* 1 \leq S_i, X \leq 10^{5}
* S_i are pairwise distinct.

Input

Input is given from Standard Input in the following format:


N X
S_1 S_2 \ldots S_{N}


Output

Print the answer.

Examples

Input

2 19
3 7


Output

3


Input

5 82
22 11 6 5 13


Output

288


Input

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009


Output

279669259
#include <bits/stdc++.h>

#define MAX_N 200
#define MAX_X 100000
#define MOD 1000000007LL
typedef long long int ll;

int n;
ll x, s[MAX_N], dp[MAX_X + 1], inv[MAX_N + 1];


int main() {
  std::cin >> n >> x;
  for(int i = 0; i < n; ++i) {
    std::cin >> s[i];
  }

  inv[1] = 1;
  for(int i = 2; i <= MAX_N; ++i) {
    inv[i] = MOD - (MOD / i) * inv[MOD % i] % MOD;
  }

  for(int i = 1; i <= x; ++i) {
    int cnt = 0;
    for(int j = 0; j < n; ++j) {
      if(s[j] <= i) {
        ++cnt;
        dp[i] = (dp[i] + dp[i % s[j]]) % MOD;
      }
    }
    if(cnt == 0) {
      dp[i] = i;
    } else {
      dp[i] = inv[cnt] * dp[i] % MOD;
    }
  }

  ll ans = dp[x];
  for(int i = 2; i <= n; ++i) {
    ans = ans * i % MOD;
  }

  std::cout << ans << std::endl;
}
