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;

typedef long long ll;
typedef pair<int,int> P;

const ll INF=1e18;
const int MOD=1e9+7;

ll mod_pow(ll x, ll n){ //べき乗
    ll ans=1;
    x%=MOD;
    while(n!=0){
        if(n&1) ans=ans*x%MOD;
        x=x*x%MOD;
        n=n>>1;
    }
    return ans%MOD;
}

int main(){
    int N,K; cin >> N >> K;
    ll a[N];
    for(int i=0;i<N;i++){
        cin >> a[i];
    }
    sort(a,a+N);
    int l=0; int r=N-1;
    ll ans=1;
    if(K%2==1){
        if(a[N-1]<0){
            for(int i=N-1;i>N-1-K;i--){
                ans*=a[i];
                ans%=MOD;
            }
            cout << (ans+MOD)%MOD << endl;
            return 0;
        }else{
            r--; K--;
        }
    }
    ll cl=0; ll cr=0;
    while(K){
        cl=a[l]*a[l+1];
        cr=a[r]*a[r-1];
        if(cl>cr){
            l+=2;
        }else{
            r-=2;
        }
        K-=2;
    }
    for(int i=0;i<l;i++){
        ans*=a[i];
        ans%=MOD;
    }
    for(int i=N-1;i>r;i--){
        ans*=a[i];
        ans%=MOD;
    }
    cout << (ans+MOD)%MOD << endl;
}