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"
#define in std::cin
#define out std::cout
#define rep(i,N) for(LL i=0;i<N;++i)
typedef long long int LL;

const LL mod = 1000000007;
LL N, X;
std::vector<LL>S;
std::vector<std::vector<LL>>memo;

LL dp(LL i, LL j)
{
	if (j == N) return i;
	if (memo[i][j] != -1) return memo[i][j];
	LL res1 = dp(i%S[j], j + 1);
	LL res2 = (dp(i, j + 1)*(N - j - 1)) % mod;
	return memo[i][j] = (res1 + res2) % mod;
}

int main()
{
	in >> N >> X;
	S.resize(N);
	rep(i, N) in >> S[i];

	memo.resize(X + 1, std::vector<LL>(N + 1, -1));
	std::sort(S.begin(), S.end(), std::greater<LL>());
	out << dp(X, 0) << std::endl;
}
