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 <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long LL;

const int N = 200010, mod =1e9+7;

int a[N];

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

    sort(a, a + n);

    int l  = 0, r = n - 1;
    int ans = 1;
    int sign  = 1;

    if(k % 2)
    {
        ans = a[r];
        r --;
        k --;

        if(ans < 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)
        {
            ans = x % mod * ans % mod;
            l += 2;
        }
        else
        {
            ans = y % mod * ans % mod;
            r -= 2;
        }
        k -= 2;
    }
    ans%=mod;
    ans=(ans+mod)%mod;
    cout << ans << endl;
    return 0;
}
