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 <cstdlib>

int compar(const void *a, const void *b)
{
    if (*(long *)a == *(long *)b) return 0;
    return (*(long *)a - *(long *)b > 0) ? 1 : -1;
}

int main()
{
    const long a = 1000000000+7;
    int N, X;
    std::cin >> N >> X;
    long S[N];
    for(int i=0; i<N; i++)
        std::cin >> S[i];
    qsort(S, N, sizeof(long), compar);

    //sum(X;S1,..,SN) = sum(X%SN;S1,..SN-1) + (N-1)sum(X;S1,..,SN-1)
    long sum[X+1][N-1];
    for(int i=0; i<=X; i++){
        sum[i][0] = i % S[0];
        for(int j=1; j<N; j++){
            sum[i][j] = ( sum[i%S[j]][j-1] + j*sum[i][j-1] ) % a;
        }
    }

    std::cout << sum[X][N-1] << std::endl;
    return 0;
}
