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 maxn = 2e5+9;
const int mod = 1e9+7;

int main(void){
    ll n, k; scanf("%lld%lld", &n, &k);
    ll a[maxn];
    ll ans = 1;
    ll sum[maxn];
    
    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);

    return 0;
}
