Recently Maxim has found an array of n integers, needed by no one. He immediately come up with idea of changing it: he invented positive integer x and decided to add or subtract it from arbitrary array elements. Formally, by applying single operation Maxim chooses integer i (1 ≤ i ≤ n) and replaces the i-th element of array ai either with ai + x or with ai - x. Please note that the operation may be applied more than once to the same position.

Maxim is a curious minimalis, thus he wants to know what is the minimum value that the product of all array elements (i.e. <image>) can reach, if Maxim would apply no more than k operations to it. Please help him in that.

Input

The first line of the input contains three integers n, k and x (1 ≤ n, k ≤ 200 000, 1 ≤ x ≤ 109) — the number of elements in the array, the maximum number of operations and the number invented by Maxim, respectively.

The second line contains n integers a1, a2, ..., an (<image>) — the elements of the array found by Maxim.

Output

Print n integers b1, b2, ..., bn in the only line — the array elements after applying no more than k operations to the array. In particular, <image> should stay true for every 1 ≤ i ≤ n, but the product of all array elements should be minimum possible.

If there are multiple answers, print any of them.

Examples

Input

5 3 1
5 4 3 5 2


Output

5 4 3 5 -1 


Input

5 3 1
5 4 3 5 5


Output

5 4 0 5 5 


Input

5 3 1
5 4 4 5 5


Output

5 1 4 5 5 


Input

3 2 7
5 4 2


Output

5 11 -5 
from Queue import PriorityQueue

def pull(i):
    global sign
    if L[i] < 0:
        L[i]+= x
        if L[i]>=0:
            sign*= -1
    elif L[i] > 0:
        L[i]-= x
        if L[i]<0:
            sign*= -1
    elif sign < 0:
        L[i]+= x
    else:
        L[i]-= x
        sign = -1
def push(i):
    global sign
    if L[i] > 0:
        L[i]+= x
    elif L[i] < 0:
        L[i]-= x
    elif sign < 0:
        L[i]+= x
    else:
        L[i]-= x
        sign = -1

n,k,x = map(int,raw_input().split())
L = list(map(int,raw_input().split()))
sign = 1
for q in L:
    if q<0:
        sign*= -1
for i in xrange(n):
    if L[i] == 0:
        if k == 0:
            break
        k-= 1
        push(i)
ini = min(xrange(n), key=lambda i: abs(L[i]))
while (sign > 0 or not L[ini]) and k > 0:
    k-= 1
    pull(ini)

Q = PriorityQueue()
for i in xrange(n):
    Q.put((abs(L[i]),i))
while k > 0:
    k-= 1
    v,i = Q.get()
    push(i)
    Q.put((abs(L[i]),i))
print(' '.join(map(str,L)))