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 ll;
#define INF (1<<30)
#define INFLL (1ll<<60)
typedef pair<int, int> P;
typedef pair<int, P> E;
#define MOD (1000000007ll)
#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a += b;
	if(a>MOD){
		a -= MOD;
	}
}

int n;
ll s[225],dp[225][100100];

int main(void){
	int n,x,i,j;
	ll ans=0ll;
	cin >> n >> x;
	for(i=0; i<n; ++i){
		cin >> s[i];
	}
	sort(s,s+n);
	dp[n][x] = 1ll;
	for(i=n; i>0; --i){
		for(j=0; j<=x; ++j){
			add_mod(dp[i-1][j%s[i-1]],dp[i][j]);
		}
		for(j=0; j<=x; ++j){
			mul_mod(dp[i][j],i-1);
			add_mod(dp[i-1][j],dp[i][j]);
		}
	}
	for(j=0; j<=x; ++j){
		mul_mod(dp[0][j],j);
		add_mod(ans,dp[0][j]);
	}
	cout << ans << endl;
	return 0;
}
