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

import java.io.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws Exception {
        solve(System.in, System.out);
    }

    static void solve(InputStream is, PrintStream os) {
        // Your code here!
        Scanner sc = new Scanner(is);
        int N = sc.nextInt();
        int K = sc.nextInt();
        List<Long> list = new ArrayList<>();
        for(int i = 0; i < N; i++) {
            list.add((long)sc.nextInt());
        }
        Collections.sort(list, Collections.reverseOrder());

        int num = 0;
        int pi = 0;
        int mi = N-1;
        List<Long> ansList = new ArrayList<>();

        if(list.get(0) < 0 && K % 2 == 1) {
            for(int i = 0; i < K; i++) {
                ansList.add(list.get(i));
            }
            num = K;
        }
        while(num < K) {
            if(K-num == 1) {
                ansList.add(list.get(pi));
                break;
            }
            if((list.get(pi) * list.get(pi+1) < list.get(mi) * list.get(mi-1)) || (pi+2 < N && K % 2 == 1 && list.get(pi+2) < 0)) {
                ansList.add(list.get(mi));
                ansList.add(list.get(mi-1));
                mi -= 2;
            } else {
                ansList.add(list.get(pi));
                ansList.add(list.get(pi+1));
                pi += 2;
            }
            num += 2;
        }
        int MOD = 1000000007;
        long ans = 1;

        for(Long l : ansList) {
            ans = ans * l % MOD;
        }

        if(ans < 0)
            os.println(ans + MOD);
        else
            os.println(ans);

    }


}