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 <vector>
#include <algorithm>
#include <cstdint>

using Int = std::int64_t;

constexpr Int MOD = 1e9 + 7;

int main() {
	Int N, X;
	std::cin >> N >> X;

	std::vector<Int> S(N);
	for (auto&& e : S)
		std::cin >> e;

	std::sort(S.begin(), S.end());

	// dp[i][x] := 最初が x のときに i 個目まで見たときの総和
	std::vector<std::vector<Int>> dp(N + 1, std::vector<Int>(X + 1));
	for (Int x = 0; x < X + 1; ++x)
		dp[0][x] = x;

	for (Int i = 1; i < N + 1; ++i) {
		for (Int x = 0; x < X + 1; ++x) {
			// 前に挿入
			dp[i][x] += dp[i - 1][x % S[i - 1]];
			dp[i][x] %= MOD;
			// 後ろに挿入
			dp[i][x] += (i - 1) * dp[i - 1][x];
			dp[i][x] %= MOD;
		}
	}

	std::cout << dp[N][X] << std::endl;
}