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
ans = 1

n, k = map(int, input().split())
a = list(map(int, input().split()))

if n == k:
    for x in a:
        ans *= x
        ans %= MOD
    print(ans % MOD)
    exit()

pos = []
neg = []

for x in a:
    if x >= 0:
        pos.append(x)
    else:
        neg.append(x)

pos.sort(reverse=True)
neg.sort()

if len(pos) == 0 and k % 2:
    for i in range(1, k+1):
        ans *= neg[-i]
        ans %= MOD
    print(ans % MOD)
    exit()

pi = 0
ni = 0
if k % 2:
    ans *= pos[pi]
    pi += 1
    k -= 1

while k > 0:
    if pi < len(pos) - 1:
        sp = pos[pi] * pos[pi + 1]
    else:
        sp = 0
    
    if ni < len(neg) - 1:
        sn = neg[ni] * neg[ni + 1]
    else:
        sn = 0
    
    if sp > sn:
        ans *= sp
        pi += 2
    else:
        ans *= sn
        ni += 2
    
    ans %= MOD
    k -= 2

print(ans % MOD)
