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<iostream>
#include<algorithm>

#define ll long long

using namespace std;

const int N = 200000 + 10;
const int mod = 1e9 + 7;
ll n,k;

ll num[N];

int main()
{
	cin>>n>>k;
	for(int i=0; i<n; i++) scanf("%lld", &num[i]);
	sort(num, num+n);
	ll ans = 1;
	ll w = 1;
	int l = 0, r = n-1;
	if(k & 1) ans = num[r--],k--;
	if(ans < 0) w = -1;
	while(k)
	{
		ll x = num[l] * num[l+1];
		ll y = num[r] * num[r-1];
		if(x*w > y*w) ans = (ans * (x % mod)) % mod, l+=2;
		else ans = (ans * (y % mod)) % mod, r-=2;
		k-=2;
	}
	cout<<(ans % mod + mod)% mod;
	return 0;
}