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;

#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define debug(x) cout << #x << ": " << x << endl;

const ll 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.rbegin(), S.rend());

    vector<vector<ll>> dp(N + 1, vector<ll>(X + 1, 0));
    dp[0][X] = 1;

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

    ll ans = 0;
    for (int i = 0; i <= X; i++) {
        (ans += (i*dp[N][i])%MOD) %= MOD;
    }
    cout << ans << endl;

    return 0;
}