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
N,K = map(int,input().split())
A = [int(a) for a in input().split()]
Ap, Am, A0 = [],[],[]
for a in A:
    if a>0: Ap.append(a)
    elif a<0 : Am.append(a)
    else: A0.append(a)
mod = 10**9+7

ans = 1
if N==K:
    for a in A:
        ans = (ans*a)%mod
    print(ans)
    exit()

if len(Ap)==0 and K%2==1:
    if len(A0)==0:
        A.sort()
        A.reverse()
        for i in range(K):
            ans = (ans*A[i])%mod
        print(ans)
        exit()
    else:
        print(0)
        exit()

Ap.sort()
Ap.reverse()
Am.sort()
if K%2==1:
    ans = Ap[0]
    Ap = Ap[1:]
    K -= 1

if K > len(Ap)+len(Am):
    print(0)
    exit()
if K == len(Ap)+len(Am) and len(Am)%2==1:
    print(0)
    exit()

Apair = [Ap[i]*Ap[i+1] for i in range(0,len(Ap)-1,2)]
for i in range(0,len(Am)-1,2):
    Apair.append(Am[i]*Am[i+1])
Apair.sort()
Apair.reverse()
for i in range(K//2):
    ans = (ans*Apair[i])%mod
print(ans)