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 int md = 1e9+7;
int n, x, s[205];
long long memo[205][100005];
bool used[205][100005];
long long solve(int v, int m){
    if(!m) return v % s[m];
    if(used[m][v]) return memo[m][v];
    used[m][v] = true;
    return memo[m][v] = (solve(v%s[m], m-1) + solve(v, m-1) * m) % md;
}
int main(){
    scanf("%d%d", &n, &x);
    for(int i = 0; i < n; i++) scanf("%d", s+i);
    sort(s, s+n);
    printf("%lld\n", solve(x,n-1));
}