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<iostream>
#include<cstdio>
#include<algorithm>
#define int long long
using namespace std;

typedef long long LL ;
const int N = 200010 , mod = 1000000007;
int a[N];


signed main()
{
    int n , k ;
    scanf("%lld%lld",&n,&k);
    for(int i = 0 ; i < n ; i ++) scanf("%lld",&a[i]);

    sort(a,a + n);

    LL res = 1 ;
    int l = 0 , r = n - 1 ;
    int sign = 1 ;
    if(k % 2 )
    {
        res =  a[r]; 
        r -- ;
        k -- ;

        if(res < 0) sign = -1;
    }
    while(k)
    {
        LL x = (LL)a[l] * a[l + 1] , y = (LL)a[r] * a[r - 1];
        if(x * sign > y * sign)
        {
            res = x % mod * res % mod; 
            l += 2;                                
        }
        else 
        {
            res = y % mod * res % mod; 
            r -= 2; 
        }
        k -= 2; 
    }
    printf("%lld",(res%mod+mod)%mod);
    return 0;
}