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 <algorithm>
#include <iostream>
using namespace std;
typedef long long int ll;
const ll inf = 1e9+7;
ll maxProductSubarrayOfSizeK(ll A[], int n, int k)
{
    sort(A, A + n);
    ll product = 1;
    if (A[n - 1] == 0 && (k & 1))
        return 0;
    if (A[n - 1] <= 0 && (k & 1)) {
        for (int i = n - 1; i >= n - k; i--)
            product = ((product * A[i])%inf + inf)%inf;
        return product;
    }
    int i = 0;
    int j = n - 1;
    if (k & 1) {
        product = ((product * A[j])%inf + inf)%inf;
        j--;
        k--;
    }
    k >>= 1;
    for (int itr = 0; itr < k; itr++)
    {
        ll left_product = A[i] * A[i + 1];
        ll right_product = A[j] * A[j - 1];
        if (left_product > right_product) {
            product = ((product * (left_product%inf))%inf + inf)%inf;
            i += 2;
        }
        else {
            product = ((product * (right_product%inf))%inf + inf)%inf;
            j -= 2;
        }
    }
    return product;
}
int main()
{
    int n,k;
    cin>>n>>k;
    ll a[n];
    for(int i=0;i<n;i++)
        cin>>a[i];
    cout << maxProductSubarrayOfSizeK(a, n, k)<<endl;
}
