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;
const int maxn=200009;
const int P=1000000007;

int T,K;
int n,m;
int a[maxn];
int b[maxn];

void work1(){
	long long ans=1;
	for(int i=1;i<=n;++i)ans=ans*a[i]%P;
	for(int i=1;i<=m;++i)ans=ans*b[i]%P;
	if(m&1)ans=(P-ans)%P;
	cout<<ans<<endl;
}
void work2(){
	long long ans=1;
	for(int i=1;i<=K;++i)ans=ans*b[i]%P;
	ans=(P-ans)%P;
	cout<<ans<<endl;
}

int main(){
	cin>>T>>K;
	
	for(int i=1;i<=T;++i){
		int x;cin>>x;
		if(x>=0){
			a[++n]=x;
		}else{
			b[++m]=-x;
		}
	}
	sort(a+1,a+1+n);
	sort(b+1,b+1+m);
	if(T==K){
		work1();return 0;
	}
	if(n==0&&K%2==1){
		work2();return 0;
	}
	long long ans=1;
	if(K&1){
		--K;ans=a[n--];
	}
	while(K){
		long long x=-1,y=-1;
		if(n>=2){
			x=1LL*a[n]*a[n-1];
		}
		if(m>=2){
			y=1LL*b[m]*b[m-1];
		}
		if(x>y){
			ans=x%P*ans%P;n-=2;
		}else{
			ans=y%P*ans%P;m-=2;
		}
		K-=2;
	}
	printf("%lld\n",ans);
	return 0;
}