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<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int N = 2e5 + 10;
const int mod = 1e9 + 7;
ll q[N]; 
int n, k;

int main()
{
	scanf("%d%d", &n, &k);
	for(int i = 1; i <= n; i++) scanf("%lld", &q[i]);
	
	sort(q + 1, q + 1 + n);
	
	ll res = 1;
	if(n == k || q[n] < 0) {
		//奇数就选绝对值尽量小，偶数就选绝对值尽量大 
		if(k & 1) for(int i = n - k + 1; i <= n; i++) res = res * q[i] % mod;
		else for(int i = 1; i <= k; i++) res = res * q[i] % mod;
	}
	else {
		int l = 1, r = n;
		if(k & 1) res = res * q[r] % mod, r--, k--;
		while(k) {
			if(q[l] * q[l + 1] > q[r] * q[r - 1]) res = res * q[l] % mod * q[l + 1] % mod, l += 2;
			else  res = res * q[r] % mod * q[r - 1] % mod, r -= 2;
			k -= 2;
		}
	}
	
	res = (res % mod + mod) % mod;
	printf("%lld\n", res);
	return 0;
}