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

if n==k:
  ans=1
  for q in a:
    ans*=q
    ans%=mod
  print(ans)
  exit()
  
if all(q>=0 for q in a):
  ans=1
  a.sort()
  for _ in range(k):
    ans*=a.pop()
    ans%=mod
  print(ans)
  exit()

if all(q<0 for q in a):
  ans=1
  a.sort()
  if k%2==0:
    for i in range(k):
      ans*=a[i]
      ans%=mod
  else:
    for _ in range(k):
      ans*=a.pop()
      ans%=mod
  print(ans)
  exit()
  
pos=[]
neg=[]
for q in a:
  if q>=0:
    pos.append(q)
  else:
    neg.append(q)

pos.sort()
neg.sort()
neg=neg[::-1]

kk=k
if kk%2==1:
  ans=pos.pop()%mod
  kk=kk-1
else:
  ans=1

while kk>0:
  if len(pos)<2:
    ans=ans*neg.pop()%mod*neg.pop()%mod
    kk-=2
  elif len(neg)<2:
    ans=ans*pos.pop()%mod*pos.pop()%mod
    kk-=2
  else:
    if pos[-1]*pos[-2]>=neg[-1]*neg[-2]:
      ans=ans*pos.pop()%mod*pos.pop()%mod
      kk-=2
    else:
      ans=ans*neg.pop()%mod*neg.pop()%mod
      kk-=2
      
print(ans)
