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<iostream>
#include<unordered_map>
#include<vector>
#include<algorithm>

using namespace std;

const auto mod = 1000000007L;

typedef long long ll;
ll key(ll x, ll n) {
    ll maxN = 200;
    return x*maxN + n;
}


ll f(ll x, ll n, vector<ll> const &s, std::unordered_map<ll, ll> &dp) {
    auto k = key(x, n);
    auto sn = s[n];
    if (dp.find(k) == dp.end()) {
        dp.emplace(k, n == 0 ? (x%sn) : (((n*f(x, n-1, s, dp))%mod + f(x%sn, n-1, s, dp))%mod));
    }
    return dp[k]%mod;
}

int main() {
    ll N;
    cin >> N;
    ll X;
    cin >> X;
    auto S = vector<ll>(N);
    for(size_t i = 0; i < N; i++){
        cin >> S[i];
    }
    sort(S.begin(), S.end());
    auto dp = std::unordered_map<ll, ll>();
    
    cout << (f(X, N-1, S, dp)%mod);
}