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;
typedef long long lint;

const lint MOD = (lint) 1e9 + 7;
lint N, X, S[205], dp[205][100005];

int main(){
    ios::sync_with_stdio(false), cin.tie(nullptr);
    cin >> N >> X;
    for(int i=0;i<N;i++) cin >> S[i];

    sort(S, S+N); reverse(S, S+N);

    dp[0][X] = 1;
    for(int i=0;i<N;i++){
        for(int j=0;j<=X;j++){
            dp[i+1][j%S[i]] = (dp[i+1][j%S[i]]+dp[i][j]) % MOD;
            dp[i+1][j] = (dp[i+1][j]+dp[i][j]*(N-i-1)) % MOD;
        }
    }

    lint ans = 0;
    for(int i=0;i<=X;i++) ans = (ans+i*dp[N][i]) % MOD;

    cout << ans << endl;
    return 0;
}