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, = map(int,input().split())

B = [a for a in A if a>=0]
B.sort()
C = [a for a in A if a<0]
C.sort(reverse = True)

ans = 1
MOD = 10**9+7

if len(B)==0 and K%2==1:
    C.sort()
    for _ in [0]*K:
        ans *= C.pop()
        ans %= MOD
    print(ans)
    exit()

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

while K>=2:
    if len(B)>=2 and len(C)>=2:
        if B[-1]*B[-2] > C[-1]*C[-2]:
            ans *= B.pop()*B.pop()%MOD
            ans %= MOD
            K -= 2
        else:
            ans *= C.pop()*C.pop()%MOD
            ans %= MOD
            K -= 2
    elif len(C)>=2:
        ans *= C.pop()*C.pop()%MOD
        ans %= MOD
        K -= 2
    else:
        ans *= B.pop()
        ans %= MOD
        K -=1
if K==1:
    ans *= B.pop()
    ans %= MOD

ans %= MOD
print(ans)