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, *A = map(int, open(0).read().split())

MOD = 10 ** 9 + 7
s = []  # v >= 0
t = []  # v < 0
for i in range(N):
    if A[i] < 0:
        t.append(A[i])
    else:
        s.append(A[i])
        
ok = False  # ans > 0
if len(s) > 0:
    if N == K:
        ok = len(t) % 2 == 0
    else:
        ok = True
else:
    ok = K % 2 == 0

ans = 1
if not ok:
    x = sorted(A, key=lambda x: abs(x))
    for i in range(K):
        ans = ans * x[i] % MOD
else:
    s.sort()
    t.sort(key=lambda x: abs(x))
    if K % 2 == 1:
        ans = ans * s.pop() % MOD
        
    p = []
    while len(s) >= 2:
        x = s.pop() * s.pop()
        p.append(x)
    
    while len(t) >= 2:
        x = t.pop() * t.pop()
        p.append(x)

    p.sort(reverse=True)
    for i in range(K // 2):
        ans = ans * p[i] % MOD
    
print(ans)

