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 lli;
typedef vector<int> Vi;
typedef vector<lli> Vl;
typedef pair<int, int> Pii;
typedef pair<lli, lli> Pll;


//===

const int MOD = (int)1e9 + 7;


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

	sort(S.begin(), S.end());

	Vl dp(X + 1);
	for (int x = 0; x <= X; ++x) dp[x] = x;

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

	cout << dp[X] << endl;
}