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;
const long long int MOD = 1e9 + 7;

int main(){
    int n, x;
    cin >> n >> x;

    vector<long long int> s(n);
    for(int i=0; i<n; i++){
        cin >> s[i];
    }
    sort(s.begin(),s.end());

    vector<vector<long long int>> dp(n+1, vector<long long int>(x+1));
    for(int j=0; j<=x; j++){
        dp[0][j] = j;
    }

    for(int i=0; i<n; i++){
        for(int j=0; j<=x; j++){
            dp[i+1][j] = (
                dp[i][j % s[i]] // when s[i] is chosen first among s[0] ~ s[i]
              + dp[i][j] * ((i-0+1) - 1) // if not
            ) % MOD;
        }
    }

    cout << dp[n][x] << endl;
    return 0;
}