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 MOD 1000000007
using namespace std;

long long int solve(vector<long long int> a,int n,int k) {
    sort(a.begin(),a.end());
//    case 1
    if(a[n-1]==0 && k&1) {
        return 0;
    }

    //case 2
    if(a[n-1]<0 && k%2!=0) {
        long long int prod = 1;
        for(int i=n-1;i>=(n-k);i--) {
            prod = (a[i]*prod)%MOD;
        }
        return ((prod%MOD)+MOD)%MOD;
    }
    long long int prod=1;
    int i=0;
    int j=n-1;
    if(a[n-1]>0 && k%2!=0) {
        prod = (prod*a[n-1])%MOD;
        k--;
        j--;
    }

    k = k/2;

    for(int p=0;p<k;p++) {
        long long int left = a[i]*a[i+1];
        long long int right = a[j]*a[j-1];
        if(left>right) {
            prod=prod * a[i]%MOD * a[i+1]%MOD;
            i+=2;
        }
        else {
            prod = prod * a[j]%MOD * a[j-1]%MOD;
            j-=2;
        }
    }
    if(prod<0)
        return ((prod%MOD)+MOD)%MOD;
    else
        return prod%MOD;
}
int main() {
    int n;
    cin>>n;
    int k;
    cin>>k;
    vector<long long int> a(n);
    for(int i=0;i<n;i++) {
        cin>>a[i];
    }
    cout<<solve(a,n,k)%MOD<<'\n';
    return 0;
}