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())
X = list(map(int, input().split()))
MOD = 10 ** 9 + 7

pos = sorted(v for v in X if v >= 0)
neg = sorted(-v for v in X if v < 0)

ok = False  # True: ans>=0, False: ans<0
if pos:
    if N == K:
        # Select all -> number of negatives must be even
        ok = len(neg) % 2 == 0
    else:
        ok = True
else:
    # All negative and even number is selected
    ok = K % 2 == 0

ans = 1
if ok:
    # ans >= 0
    if K % 2 == 1:
        ans = ans * pos.pop() % MOD

    # 答えは正になる→二つの数の積は必ず正になる．
    cand = []
    while len(pos) >= 2:
        x = pos.pop() * pos.pop()
        cand.append(x)

    while len(neg) >= 2:
        x = neg.pop() * neg.pop()
        cand.append(x)

    cand.sort(reverse=True)
    for i in range(K // 2):
        ans = ans * cand[i] % MOD
else:
    # ans <= 0
    cand = sorted(X, key=lambda x: abs(x))
    for i in range(K):
        ans = ans * cand[i] % MOD

print(ans)
