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
ans = 1

#全部取る
if n == k:
    for x in a:
        ans *= x
        ans %= MOD
    print(ans % MOD)

#全部負かつ奇数個取る
elif max(a) < 0 and k % 2:
    a.sort()
    for i in range(1, k+1):
        ans *= a[-i]
        ans %= MOD
    print(ans % MOD)

else:
    pos = []
    neg = []
    
    for x in a:
        if x >= 0:
            pos.append(x)
        else:
            neg.append(x)
    
    pos.sort(reverse=True)
    neg.sort()
    
    
    if k % 2:
        ans *= pos.pop(0)
        k -= 1
     
    #2個ずつ取る
    num = []
    for x, y in zip(pos[::2], pos[1::2]):
        num.append(x * y)
    for x, y in zip(neg[::2], neg[1::2]):
        num.append(x * y)

    num.sort(reverse=True)

    for i in range(k // 2):
        ans *= num[i]
        ans %= MOD
    
    print(ans % MOD)
    