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;
#define rep(i,n) for(int i = 0;i < n;i++)
#define ALL(a) a.begin(),a.end()
typedef long long ll;
ll n,k, y,x, w = 1,ans = 1;
const int MOD = 1000000007;
int main(void) {
	cin >> n >> k;vector<ll> a(n);
	rep(i, n) cin >> a[i];
	sort(ALL(a)); int l = 0,r = n-1;
	if (k % 2) {
		ans = a[r--]; --k;
		if (ans < 0) w = -1;
	}
	while (k) {
		x = a[l] * a[l + 1], y = a[r] * a[r - 1];
		if (x * w > y * w) {
            ans *= (x%MOD); ans %= MOD; l += 2;
		}
		else {
            ans *= (y%MOD); ans %= MOD; r -= 2;
		}k -= 2;
	}cout << (ans+MOD)%MOD << endl;
}