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;
#define mk make_pair
#define PII pair<ll,int>
#define PB push_back
const int maxn=2e5+9;
const int mod=1e9+7;
ll k,n,a[maxn],ans;
ll sum[maxn];
int main()
{
	ans=1;
	scanf("%lld%lld",&n,&k);
	for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
	sort(a+1,a+1+n);
	int fh=1,l=1,r=n;
	if(k&1)
	{
		ans=a[n];if(a[n]<0)fh=-1;k--;r--;
	}
	while(k)
	{
		ll s1=a[l]*a[l+1],s2=a[r]*a[r-1];
		if(s1*fh>s2*fh)ans=(ans*(s1%mod))%mod,l+=2;
		else ans=(ans*(s2%mod))%mod,r-=2;
		k-=2;
	}
	ans=(ans+mod)%mod;
	printf("%lld\n",ans);
}