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
mod = 10**9+7
def func(A, n, k):
    A.sort()
    product = 1
    if (A[n - 1] == 0 and (k & 1)):
        return 0
    if (A[n - 1] <= 0 and (k & 1)) :
        for i in range(n - 1, n - k - 1, -1):
            # print(A[i])
            product = (product*A[i])%mod
        return product%mod
    i = 0
    j = n - 1
    if (k & 1):
        product = (product*A[j])%mod
        j-= 1
        k-=1
    k >>= 1
    for itr in range( k):
        left_product = (A[i] * A[i + 1])
        right_product = (A[j] * A[j - 1])
        if (left_product > right_product):
            product = (product*(left_product)%mod)%mod
            i += 2
        else:
            product = ((right_product%mod)*product)%mod
            j -= 2
    return product%mod 

n,k = list(map(int,input().split()))
arr = list(map(int,input().split()))
ans = func(arr,n,k)
print(ans)
# print(-6%mod)