How to create an array from two 2d arrays, based in conditionals and random selection with PYTHON

I´m trying to create an array using two 2d arrays and conditionals. The first array created randomly with numpy is:

A = [[0 0 0 1 0 1 1 0 0 1 0],
     [0 0 1 1 1 1 1 1 0 1 1],
     [0 0 0 1 0 1 1 1 0 0 0],
     [1 1 0 1 0 0 0 1 1 1 0]]

and the second array is:

B = ["a","b","c","d"]

I´m trying to create an array, selecting randomly only "1" value in each column (the row containing "1" doesn´t matter). When I find "1", the position (in selected row) must be linked to array "B", take the value in "B" and finally allocate it in array "C". For example, evaluating column "0", the only possible value is A[0,3]=1, so B=["d"] (the only possible value) and this value must be the 1st value for array "C". Column "3" can take any value from "B".

For example the full array I´m looking for could be the following one:

C= ["d","d","b","a","b","c","a","d","d","a","b"]

I´m trying to create "C" with the following code:

import numpy as np
A=np.random.randint(2, size=(4,11)) 
A=np.array(A)

C=[] 
var=0

B=["a1","b1","c2","d2"]

for i in range(11):
    C.append(var)
    R=np.random.randint(0,4)             
    if A[R,0+i]==1:
        var=B[R]        
    else:
        var=0
print(C)

The result is the following one:

[0, 0, 'a1', 'a1', 'd2', 0, 'd2', 'd2', 'd2', 0, 0]

This code doesn´t complete the work, I can´t find "1" in several columns. I´ve been trying different methods, including: coordinates, loops and generators. But I can´t find one that really works.

I´ll be very grateful if you can help me.

Thank you.