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 rep(i, n) for (int i = 0; i < n; i++)
#define rrep(i, n) for (int i = n - 1; i >= 0; i--)
using namespace std;
#define INF ((1<<30)-1)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long ll;
typedef pair<ll, ll> P;
const int MOD = 1000000007;
const int MOD2 = 998244353;

ll a[200010];

int main(){
    int n, k;
    cin >> n >> k;
    rep(i, n) cin >> a[i];
    sort(a, a+n);

    int l = 0, r = n - 1, flag = 1;
    ll ans = 1;

    if (k % 2 == 1){
        ans = a[r];
        r--;
        k--;
        if (ans < 0) flag = -1;
    }

    while(k > 0){
        ll x = a[l] * a[l+1], y = a[r] * a[r-1];
        // cout << x << " " << y << endl;
        if (x * flag > y * flag){
            x %= MOD;
            ans *= x;
            ans %= MOD;
            l += 2;
        }
        else {
            y %= MOD;
            ans *= y;
            ans %= MOD;
            r -= 2;
        }
        k -= 2;
    }

    cout << (ans + MOD) % MOD << endl;
    return 0;
}
