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
MOD = 10 ** 9 + 7

N, K = map(int, input().split())
A = list(map(int, input().split()))
ans = 1
if N == K:
    for a in A:
        ans = ans * a % MOD
    print(ans)
    exit(0)

minus = []
plus = []
for a in A:
    if a < 0:
        minus.append(a)
    else:
        plus.append(a)

if len(minus) == N:
    if K % 2 == 0:
        A.sort()
    else:
        A.sort(reverse=True)
    for i in range(K):
        ans = ans * A[i] % MOD
    print(ans)
    exit(0)

minus.sort(reverse=True)
plus.sort()

if  K % 2:
    ans *= plus.pop()

B = []

while len(minus) > 1:
    a = minus.pop()
    b = minus.pop()
    B.append(a * b)

while len(plus) > 1:
    a = plus.pop()
    b = plus.pop()
    B.append(a * b)

B.sort()

for i in range(K // 2):
    ans = ans * B.pop() % MOD

print(ans)
