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;
long M=1e9+7,n,k,ans=1,l,r,b=1,a[1<<18],x,y,i;
int main(){cin>>n>>k;r=n-1;
for(i=0;i<n;i++)cin>>a[i];
sort(a,a+n);
if(k%2)ans=a[r],r--,k--,b=(ans<0?-1:1);
while(k){x=a[l]*a[l+1],y=a[r]*a[r-1];
if(x*b>y*b)ans*=x%M,ans%=M,l+=2;
else ans*=y%M,ans%=M,r-=2;
k-=2;}cout<<(ans+M)%M<<endl;
}
