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 int long long int
using namespace std;
int32_t main()
{
	#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
	#endif

	int n,k;
	cin >> n >> k;
	int arr[n];
	for(int i=0;i<n;i++){
		cin >> arr[i];
	}
	sort(arr,arr+n);
	int ans=1;
	int mod=1000000007;
	if((k&1) && (arr[n-1]==0)){
		cout << 0 << endl;
		return 0;
	}
	if((k&1) && (arr[n-1]<0)){
		for(int i=n-1;i>=n-k;i--){
			ans=(ans*arr[i]%mod);
			if(ans<0)	ans+=mod;
		}
		cout << ans << endl;
		return 0;
	}
	int low=0,high=n-1;
	if((k&1) && (arr[n-1]>0)){
		ans=(ans*arr[high]%mod);
		if(ans<0)	ans+=mod;
		high--;k--;
	}
	k/=2;
	for(int ii=0;ii<k;ii++){
		if(arr[low]*arr[low+1]>arr[high]*arr[high-1]){
			ans=(ans*arr[low]%mod);
			if(ans<0)	ans+=mod;
			low++;
			ans=(ans*arr[low]%mod);
			if(ans<0)	ans+=mod;
			low++;
		}
		else{
			ans=(ans*arr[high]%mod);
			if(ans<0)	ans+=mod;
			high--;
			ans=(ans*arr[high]%mod);
			if(ans<0)	ans+=mod;
			high--;
		}
	}
	if(ans<0)	ans+=mod;
	ans%=mod;
	cout << ans << endl;


	return 0;
}