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>
using namespace std;
#define ll long long

ll mod = 1e9+7;

int main(){
    int N, X;
    cin >> N >> X;
    vector<int> S(N);
    for (int i = 0; i < N; i++) cin >> S[i];
    sort(S.begin(), S.end());
    reverse(S.begin(), S.end());
    vector<vector<ll>> dp(N+1, vector<ll>(X+1, 0));
    dp[0][X]++;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j <= X; j++) {
            dp[i+1][j] += (N-1-i)*dp[i][j];
            dp[i+1][j] %= mod;
            dp[i+1][j%S[i]] += dp[i][j];
            dp[i+1][j%S[i]] %= mod;
        }
    }
    ll ans = 0;
    for (int i = 1; i < S[N-1]; i++) ans = (ans + i*dp[N][i])%mod;
    cout << ans << endl;
    return 0;
}