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 int ll;
typedef pair<int, int> ii;

struct fastio {
    fastio() {
        ios::sync_with_stdio(false);
        cout << setprecision(10) << fixed;
        cin.tie(0);
    }
};

fastio _fast_io;

const int mod = 1e9 + 7;
int n, k;
const int N = 2e5 + 10;
ll a[N];

int main() {
    ll res = 1;
    cin >> n >> k;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    bool neg = false;
    sort(a, a + n);
    int l = 0, r = n - 1;
    if (k & 1) {
        res = a[n - 1];
        --k;
        --r;
        if (res < 0)
            neg = true;
    }
    while (k) {
        ll x = a[l] * a[l + 1];
        ll y = a[r] * a[r - 1];
        if ((x > y) ^ neg) {
            l += 2;
            res = (res * (x % mod)) % mod;
        } else {
            r -= 2;
            res = (res * (y % mod)) % mod;
        }
        k -= 2;
    }
    res = (res + mod) % mod;
    cout << res << endl;

    return 0;
}
