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

INF = 10 ** 9 + 7
N, K = map(int, input().split())
a = list(map(int, input().split()))
a.sort(reverse=True)

if K == 1:
    print(a[0])
    exit()

if K == N:
    ans = 1
    for i in a:
        ans *= i
        ans %= INF
    print(ans)
    exit()

if a[0] < 0:
    ans = 1
    if K % 2 == 1:
        for i in range(K):
            ans *= a[i]
            ans %= INF
    else:
        for i in range(K):
            ans *= a[-i - 1]
            ans %= INF
    print(ans)
    exit()

sei = []
hu = []
for i in a:
    if i >= 0:
        sei.append(i)
    else:
        hu.append(i)
hu.sort()
seis = []
hus = []
total = []
ans = 1

if K % 2 != 0:
    ans = sei[0] % INF
    for i in range(2, len(sei), 2):
        seis.append(sei[i] * sei[i - 1])
else:
    for i in range(1, len(sei), 2):
        seis.append(sei[i] * sei[i - 1])
for i in range(1, len(hu), 2):
    hus.append(hu[i] * hu[i - 1])

total = hus + seis
total.sort(reverse=True)
for i in range(K // 2):
    ans *= total[i]
    ans %= INF

print(ans)
