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;

using ll = long long;
const int MOD = (int) 1e9 + 7;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    unsigned long N, X;
    cin >> N >> X;

    ll S[N];
    for (int i = 0; i < N; ++i) {
        cin >> S[i];
    }
    sort(S, S +N);

    vector<vector<ll> > dp(N + 1, vector<ll>(X + 1, 0));
        for (int j = 0; j <= X; ++j) {
            dp[0][j] = j;
        }

    for (int i = 0; i < N; ++i) {
        for (int j = 0; j <= X; ++j) {
            dp[i + 1][j] += dp[i][j % S[i]];
            dp[i + 1][j] %= MOD;
            dp[i + 1][j] += dp[i][j] * i % MOD;
            dp[i + 1][j] %= MOD;
        }
    }

    cout << dp[N][X] << '\n';

    return 0;
}
