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;

using ll = int64_t;
const int MAX = 2e5;
const int MOD = 1e9 + 7;

int32_t main()
{
    ios::sync_with_stdio(false), cin.tie(nullptr);
    int n, k; cin >> n >> k;
    vector<ll> v(n);
    for (auto& it : v) cin >> it;
    int r = n-1, l = 0, sign = 1;
    ll ans = 1;

    sort (v.begin(), v.end());

    if (k%2 == 1) {
        ans = v[r];
        r--, k--;
        sign = ans < 0 ? -1 : 1;
    }

    while (k) {
        ll x = v[l] * v[l+1];
        ll y = v[r] * v[r-1];
        if (x*sign > y*sign) ans = (ans * (x%MOD))%MOD, l += 2;
        else ans = (ans * (y%MOD))%MOD, r -= 2;
        k -= 2;
    }

    cout << (ans + MOD)%MOD;


    return 0;
}