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;

const int maxn = 200 + 10;
const int maxm = 100000 + 10;
const ll MOD = 1e9 + 7;

ll N, X;

vector<vector<ll>> dp(maxn, vector<ll>(maxm, -1));
vector<ll> nums(maxn);

ll f(ll i, ll x) {
    if (i == N) {
        return x;
    }
    if (dp[i][x] != -1) {
        return dp[i][x];
    }
    ll ans = 0;
    ans += f(i + 1, x % nums[i]);
    ans += f(i + 1, x) * (N - i - 1);
    return dp[i][x] = ans % MOD;
}

int main() {
    cin >> N >> X;
    for (int i = 0; i < N; ++i) {
        cin >> nums[i];
    }
    sort(nums.begin(), nums.end(), greater<ll>());
    cout << f(0, X) << endl;
    return 0;
}