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<stdio.h>
#include<algorithm>
#pragma GCC optimize("O2")
#define rep(i,N) for(int i=0;i<(int)N;i++)
using namespace std;
const int MOD=1e9+7;
static inline int IN(void)
{
  int x=0,f=0,c=getchar();while(c<48||c>57){f^=c==45,c=getchar();}
  while(c>47&&c<58){x=x*10+c-48,c=getchar();}return f?-x:x;
}

int main()
{
  int A[200000],N=IN(),K=IN(),l,m=0,r,accum=1,sign=1;long x,y;
  rep(i,N)A[i]=IN(),m+=A[i]<0?1:0;
  sort(A,A+N);
  if(K&1)accum=A[N-1],sign=(A[N-1]<0?-1:1),N--,K--;
  l=0,r=N-1;
  while(K)
  {
    x=1l*A[l]*A[l+1],y=1l*A[r]*A[r-1];
    if(x*sign>y*sign)x%=MOD,accum=1l*accum*x%MOD,l+=2;
    else y%=MOD,accum=1l*accum*y%MOD,r-=2;
    K-=2;
  }
  return printf("%ld\n",(1l*accum%MOD+MOD)%MOD),0;
}
