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>
#define maxn 200005
#define ll long long
#define mod 1000000007
using namespace std;
ll a[maxn],n,k,fhw,l,r,ans=1;
bool cmp(ll x,ll y){return x>y;}
int main(){
	cin>>n>>k;
	for(int i=0;i<n;++i) 
		scanf("%lld",&a[i]);
	sort(a,a+n);
	l=0;r=n-1;
	if(k&1) k--,ans*=a[r--];
	if(ans<0) fhw=-1;else fhw=1;
	while(k){
		if(a[l]*a[l+1]*fhw<a[r]*a[r-1]*fhw) (ans*=a[r]*a[r-1]%mod)%=mod,r-=2;
		else (ans*=a[l]*a[l+1]%mod)%=mod,l+=2;
		k-=2;
	}
	cout<<(ans%mod+mod)%mod;
	
	return 0;
}