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 <vector>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <queue>
#include <set>
#include <map>
using namespace std;
typedef long long ll;

#include <cstdio>
#include <vector>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <queue>
#include <set>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e5+7, mod = 1e9+7;
int n, k;
int a[N];
int main()
{
    scanf("%d%d",&n,&k);
   	for(int i = 0;i < n;++i)	scanf("%d",&a[i]);
    sort(a,a + n);

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

    return 0;
}
