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>
#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;

const int MOD = 1e9 + 7;

int main() {
    int N, K;
    cin >> N >> K;
    int64_t A[N], ans = 1;
    rep(i, N) cin >> A[i];
    sort(A, A + N);

    int l = 0, r = N - 1, sign = 1;
    if (K % 2) {
        ans = A[r];
        r--;
        K--;
        if (ans < 0) sign = -1;
    }

    while (K) {
        int64_t x = A[l] * A[l+1];
        int64_t y = A[r] * A[r-1];
        if (x * sign > y * sign) {
            ans *= x % MOD;
            l += 2;
        } else {
            ans *= y % MOD;
            r -= 2;
        }
        ans %= MOD;
        K -= 2;
    }
    cout << (ans + MOD) % MOD << endl;
}