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;
const int Mod = 1000000007;
int a[200005];
int main()
{
    int n, k;
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; i++)
        scanf("%d", &a[i]);
    sort(a + 1, a + n + 1);
    int res = 1;
    if (a[n] < 0)
    {
        if (k & 1)
            for (int i = n - k + 1; i <= n; i++)
                res = 1LL * res * a[i] % Mod;
        else
            for (int i = 1; i <= k; i++)
                res = 1LL * res * a[i] % Mod;
    }
    else
    {
        int l = 1, r = n;
        if (k & 1)
            res = 1LL * res * a[r] % Mod, r--, k--;
        while (k)
        {
            if (1LL * a[l] * a[l + 1] > 1LL * a[r] * a[r - 1])
                res = 1LL * res * a[l] % Mod * a[l + 1] % Mod, l += 2;
            else
                res = 1LL * res * a[r] % Mod * a[r - 1] % Mod, r -= 2;
            k -= 2;
        }
    }
    res = (res + Mod) % Mod;
    return 0 * printf("%d\n", res);
}
