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 ll mod=1e9+7;
ll A[300001];
int main() {
    ll n,k;
	cin>>n>>k;
	
	for(int i=0;i<n;i++) cin>>A[i];
	sort(A,A+n);
	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=A[l]*A[l+1],y=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<<(ans+mod)%mod<<endl;
	return 0;
}
