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;

int main()
{
    int n, k, mod = 1e9 + 7;
    cin >> n >> k;
    vector <int> a(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }
    sort(a.begin(), a.end());
    long long ans = 1;
    int l = 0, r = n - 1, sign = 1;
    if (k % 2 == 1)
    {
        ans = a[r];
        r--;
        if (ans < 0) sign = -1;
        k--;
    }
    while (k)
    {
        long long x = (a[l] * 1ll * a[l + 1]), y = (a[r - 1] * 1ll * a[r]);
        if (sign == 1)
        {
            if (x < y)
            {
                ans = y % mod * ans % mod;
                r -= 2;
            }
            else {
                ans = x % mod * ans % mod;
                l += 2;
            }
        }
        else {
            if (x > y)
            {
                ans = y % mod * ans % mod;
                r -= 2;
            }
            else {
                ans = x % mod * ans % mod;
                l += 2;
            }
        }
        k -= 2;
    }
    cout << (ans + mod) % mod << endl;
}