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 <iomanip>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>
#include <set>
using namespace std;
#define MOD 1000000007

long long N, X;
long long dp[202][111111];

void add(long long &x, long long y){
    x = (x + y) % MOD;
}

int main(){
    cin >> N >> X;
    vector<long long> S(N);
    for(int i=0; i<N; i++)
        cin >> S[i];

    sort(S.begin(), S.end(), greater<long long>());

    dp[0][X] = 1;
    for(int i=1; i<=N; i++){
        for(int j=0; j<=100000; j++){
            add(dp[i][j], ((N-i) * dp[i-1][j]) % MOD);
        }
        for(int j=0; j<=100000; j++){
            add(dp[i][j%S[i-1]], dp[i-1][j]);
        }
    }
    long long ans = 0;
    for(int i=0; i<=100000; i++)
        add(ans, (dp[N][i] * i) % MOD);
    cout << ans << endl;

    return 0;
}