Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

* 1 \leq K \leq N \leq 2\times 10^5
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 \ldots A_N


Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1


Output

999983200
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>
using namespace std;
typedef long long ll;
#define MOD 1000000007
#define rep(i, n) for(int i=0; i<(n); ++i)



int main()
{
	int N, K; cin >> N >> K;
	vector<int> A(N);
	rep(i, N) cin >> A[i];
	sort(A.begin(), A.end());

	ll ans = 1, sign = 1;
	int l = 0, r = N - 1;
	if (K % 2) {
		ans = A[r--];
		--K;
		if (ans < 0) sign = -1;
	}
	while (K) {
		ll x = (ll)A[l] * A[l + 1];
		ll y = (ll)A[r] * A[r - 1];
		if (x * sign > y* sign) {
			ans = x % MOD * ans % MOD;
			l += 2;
		}
		else {
			ans = y % MOD * ans % MOD;
			r -= 2;
		}
		K -= 2;
	}
	cout << (MOD + ans) % MOD << endl;
	return 0;
}
