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
N,K = map(int,input().split())
A = list(map(int,input().split()))
sign = dict({-1:0,0:0,1:0})
for a in A:
    if a<0:
        sign[-1]+=1
    elif a>0:
        sign[1]+=1
    else:
        sign[0]+=1
if sign[1]==0 and K%2!=0:
    A.sort(reverse=True)
    ans = 1
    for i in range(K):
        ans *= A[i]
        ans %= MOD
elif sign[1]==0 and K%2==0:
    A.sort()
    ans = 1
    for i in range(K):
        ans *= A[i]
        ans %= MOD
else:
    A.sort()
    ans = 1
    i,j = 0,N-1
    while K>0:
        if K>1 and A[i]*A[i+1]>=A[j]*A[j-1]:
            ans *= A[i]*A[i+1]
            ans %= MOD
            i += 2
            K -= 2
        else:
            ans *= A[j]
            ans %= MOD
            j -= 1
            K -= 1
print(ans)