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 MOD 1000000007
#define fastio std::ios_base::sync_with_stdio(false);
#define ll long long
#define matrix vector <vector <ll> >

int A[210];
int dp[100010][210];

int ans(int X, int n) {
    if(n == 1) 
        return X%A[n-1];

    if(dp[X][n] != -1)  return dp[X][n];
    
    return dp[X][n] = (ans(X%A[n-1], n-1) + (1LL*ans(X, n-1)*(n-1))%MOD)%MOD;
}

int main(){

    fastio;
    
    int n, X;
    cin >> n >> X;
    for(int i = 0; i < n; i++) {
        cin >> A[i];
    }
    sort(A, A+n);

    for(int i = 0; i < 100010; i++) {
        for(int j = 0; j < 210; j++) {
            dp[i][j] = -1;
        }
    }

    cout << ans(X, n);

    return 0;
}
