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;

constexpr ll MOD = 1e9 + 7;

ll N, X;
vector<ll> s;
vector<vector<ll>> memo;

ll Rec(int idx, ll x) {
    if (idx == N) return x;
    if (memo[idx][x] != -1) return memo[idx][x];

    ll &res = memo[idx][x];
    res = Rec(idx + 1, x % s[idx]) % MOD;
    (res += Rec(idx + 1, x) * (N - idx - 1)) %= MOD;

    return res;
}

int main() {
    cin.tie(0); ios::sync_with_stdio(false);

    cin >> N >> X;
    s.resize(N);
    for (auto &s_i : s) cin >> s_i;
    sort(s.begin(), s.end(), greater<ll>());

    memo.resize(N, vector<ll>(X + 1, -1));
    cout << Rec(0, X) << endl;

    return 0;
}
