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 <iostream>
#include <algorithm>

#define P 1000000007

using namespace std;

long dp[200][100001];
long S[200];

int main(){
    long N, X;
    cin >> N >> X;
    for(int i = 0; i < N; i++){
        cin >> S[i];
    }
    sort(S, S+N);
    for(int i = 0; i <= 100000; i++){
        dp[0][i] = i%S[0];
    }
    for(int i = 1; i < N; i++){
        for(int j = 0; j <= 100000; j++){
            dp[i][j] = (dp[i-1][j]*i+dp[i-1][j%S[i]])%P;
        }
    }
    cout << dp[N-1][X] << endl;
}