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
def sgn(v):
    return (v > 0) - (v < 0)
def find_ans():
	v.sort(key=abs, reverse=True)
	ns = 1
	sg = 1
	for a in xrange(k):
	    ns *= v[a]
	    ns %= mod
	    sg *= sgn(v[a])

	if sg >= 0:
	    return ns

	if max(v) <= 0:
	    ns = 1
	    for a in xrange(-k,0):
	        ns *= v[a]
	        ns %= mod
	    return ns

	def helper_f(comp):
	    i = k-1
	    while i >= 0 and comp(v[i]): i -= 1
	    j = k
	    while j < n and not comp(v[j]): j += 1
	    if j == n: j = i
	    return i, j
	i, j = helper_f(lambda w: w >= 0)
	I, J = helper_f(lambda w: w <= 0)
	if I >= 0 and v[j] * v[I] < v[i] * v[J]:
	    i = I
	    j = J

	ns = v[j]
	for a in xrange(k):
	    if a != i:
	        ns *= v[a]
	        ns %= mod
	return ns

n, k = map(int, raw_input().strip().split())
v = map(int, raw_input().strip().split())
print(find_ans())
	