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;    

#define LL long long
const int mod = 1e9 + 7;
LL n, k, sign = 1, a[200005], x, y, l, r, ans = 1LL;

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    
    cin >> n >> k;
    for(int i = 0; i < n; i++) cin >> a[i];
    sort(a, a+n);
    r = n - 1;

    if(k % 2) {
        ans = a[r]; 
        --r, --k;
        sign = (ans < 0 ? -1 : 1);
    }        

    while(k > 0) {
        x = a[l] * a[l+1], y = a[r] * a[r-1];
        if(x * sign > y * sign) (ans *= (x % mod)) %= mod, l += 2;
        else (ans *= (y % mod)) %= mod, r -= 2;
        k -= 2; 
    }
    cout << (ans + mod) % mod;
}