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
flag=0

A.sort()

tmp1=1
tmp2=1

l=0
r=n-1
if k%2==1:
    tmp1=A[-1]%mod
    r-=1
    if A[-1]<0:
        flag=1
for i in range(k//2):
    vl=A[l]*A[l+1]
    vr=A[r]*A[r-1]
    if max(vl,vr)<0:
        flag=1
    if vl>vr:
        l+=2
        tmp1*=vl
    else:
        r-=2
        tmp1*=vr
    tmp1%=mod

from bisect import bisect_right
idx=bisect_right(A,0)
if idx==n:
    idx-=1
l=max(0,idx-1)
r=idx
for i in range(k):
    vl=A[l] if l>=0 else mod
    vr=A[r] if r<n else mod
    if abs(vl)<abs(vr) or r==n:
        l-=1
        tmp2*=vl
    else:
        r+=1
        tmp2*=vr
    tmp2%=mod

if flag==0:
    print(tmp1)
else:
    print(tmp2)

