Efficient Way to Balance Array of Integers in Python

The following code

import numpy as np
W   = 5         # any odd positive integer
L   = 7         # any positive integer
M   = (W-1)//2
arr = np.random.choice(range(W),L) - M

generates an array of length L with numbers ranging from -W to W. Now I want to amend this array such that its sum is 0 (while keeping the restriction that elements are within -W to W).

I want to achieve this by adding increments of +1 (if the initial sum is negative) or increments of -1 (if the initial sum is positive) to the elements of this array, starting from the first element of the list (and then the second, third, etc. should I need to). For example, if the initial sum is -2 (i.e. negative) and the array is [2,0,-1,...] then I cannot increment by the first element by +1 (it's already at max W=2), and thus I need to increment the second element two times, resulting in [2,2,-1,...].

Three samples:

[-1,  0,  0, -1,  2,  0, 2] ---> [-2, -1,  0, -1,  2,  0, 2]
or
[-2, -2,  1, -2,  0, -1, 2] ---> [ 2, -2,  1, -2,  0, -1, 2]
or 
[ 2,  2,  2,  2,  2,  2, 2] ---> [-2, -2, -2,  0,  2,  2, 2]

It's easy to write a few for/while loops which do this, but is there a more efficient way (perhaps a numpy function)?