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>

#define ll long long
#define fornum(A,B,C) for(A=B;A<C;A++)
#define mp make_pair
#define pii pair<int,int>
#define pll pair<ll,ll>

using namespace std;

/////////////////////////////////////////////////////
#define MOD (ll)(1e9+7)
ll N,X;
ll dp[202][101010];
ll S[222];
ll i,j,k;
int main(){
    scanf("%lld%lld", &N ,& X);
    fornum(i,0,N){
        scanf("%lld", &S[i]);
    }
    sort(S, S + N, greater<ll>());
    dp[0][X] = 1;
    fornum(i,0,N){
        fornum(j,0,X+1){
            dp[i+1][j % S[i]] =(dp[i+1][j % S[i]] + dp[i][j])%MOD;
        }
        fornum(j,0,X+1){
            dp[i + 1][j] = (dp[i+1][j]+dp[i][j] * (N-1-i)) % MOD;
        }
    }
    ll ans = 0;
    fornum(i,0,S[N-1]){
        ans = (ans+dp[N][i] * i)%MOD;
    }
    printf("%lld", ans);
    return 0;
}