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;

using i64 = int64_t;

constexpr i64 MOD = 1e9 + 7;

i64 dp[202][100005]={0};

int main(){
    int n;
    i64 x;
    cin >> n >> x;
    vector<i64> v;
    for(int i=0;i<n;++i){
        i64 s;
        cin >> s;
        v.push_back(s);
    }
    sort(v.rbegin(), v.rend());

    for(i64 i=0;i<=x;++i){
        dp[n][i] = i % v[n-1];
    }
    for(int i=n-1;i>0;--i){
        for(i64 j=0;j<=x;++j){
            dp[i][j] = ((n-i)*dp[i+1][j]) % MOD;
            dp[i][j] = (dp[i][j] + dp[i+1][j%v[i-1]]) % MOD;
        }
    }

    cout << dp[1][x] << endl;

    return 0;
}
