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 = list(map(int,input().split()))
mod = 10**9+7
A.sort()
ans = 1
if A[-1]==0 and K&1: print(0);exit()
if A[-1]<0 and K&1:
    for i in range(N-1,N-1-K,-1):
        ans =(ans*A[i])%mod
    print(ans)
    exit()
l,r = 0,N-1
if K&1:
    ans *= A[-1]
    r-=1
    K-=1
p = K//2
for i in range(p):
    lp = A[l]*A[l+1]
    rp = A[r]*A[r-1]
    if lp>rp:
        ans = (ans*lp)%mod
        l += 2
    else:
        ans = (ans*rp)%mod
        r-=2
print(ans%mod)
