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 l_ength size
const int inf = (1<<30);
const int mod = 1000000007;
using ll = long long;
using namespace std;

ll dp[210][100010];

int main(){
    int n, x; cin >> n >> x;
	vector<int> s(n);
	for( auto &k : s ) cin >> k;
	sort( s.begin(), s.end() );
	for( int k = 0; k <= x; ++k ){
		dp[0][k] = k; 
	}
	for( int i = 0; i < n; ++i ){
		for( int k = 0; k <= x; ++k ){
			dp[i+1][k] = dp[i][k]*i % mod + dp[i][k%s[i]];
			dp[i+1][k] %= mod;
		}
	}
	/* for( int i = 0; i <= n; ++i ){
		for( int k = 0; k <= x; ++k ){
			cout << dp[i][k] << ' ';
		} cout << endl;
	} */
	cout << dp[n][x] << endl;
}