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;

const int N=2e5+10, mod=1e9+7;
ll n,k,a[N],ans,flag;

int main(){
	cin>>n>>k;
	for(ll i=0;i<n;i++){
		scanf("%lld",&a[i]);
	}
	sort(a,a+n,greater<ll>());
	ll l=0, r=n-1;
	ans=1; flag=1;//注意如果开始k是偶数，flag要初始化 
	if(k%2) ans=a[l], l++, flag=(ans>=0?1:-1), k--;
//cout<<ans<<" f"<<flag<<endl;
	while(k){
//cout<<l<<" "<<r<<endl;
		ll x=a[l]*a[l+1], y=a[r]*a[r-1];
		if(flag*x>flag*y) ans=ans*(x%mod)%mod, l+=2;
		else ans=ans*(y%mod)%mod, r-=2;
		k-=2;
//cout<<x<<" "<<y<<" "<<ans<<endl;
	}
	cout<<(ans+mod)%mod<<endl;
	return 0;
}
