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+5,M=1e6+5,inf=0x3f3f3f3f,mod=1e9+7;
#define mst(a) memset(a,0,sizeof a)
#define lx x<<1
#define rx x<<1|1
#define reg register
#define PII pair<int,int>
#define fi first 
#define se second
ll a[N];
int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	for(int i=0;i<n;i++) scanf("%lld",&a[i]);
	sort(a,a+n);
	int l=0,r=n-1,w=1; 
	ll ans=1;
	if(k&1) ans=a[r--],k--,w=(ans<0?-1:1);
	while(k){
		ll x=a[l]*a[l+1],y=a[r]*a[r-1];
		if(x*w>y*w) ans=(ans*(x%mod))%mod,l+=2;
		else ans=(ans*(y%mod))%mod,r-=2;
		k-=2;
	}
	printf("%lld\n",(ans%mod+mod)%mod);
	return 0;
}