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
/*
 * @Date         : 2020-08-10 15:34:44
 * @Author       : ssyze
 * @Description  :
 */
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
const int maxn = 1e6 + 6;
int n, k;
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> n >> k;
    vector<ll> a(n);
    for (auto& x : a) cin >> x;
    sort(a.begin(), a.end());
    ll l = 0, r = n - 1, w = 1;
    ll ans = 1;
    if (k & 1) ans = a[r--], k--, w = (ans < 0 ? -1 : 1);
    while (k) {
        ll x = a[l] * a[l + 1], y = a[r] * a[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 << endl;
}