how to generate a random binary matrix with a specific condition?

if matrix A shows the number of group of ones in G (n,m) matrix like that

 G = [ 1 1 0 0 1 
       0 1 1 1 0
       1 0 1 1 1 ]

SO the A matrix will be

 A = [ 2 1
       3 0
       1 3 ]

Then i want to generate (n,m) random matrix which the ones in this Matrix depend on A in the same order they appear

one solution will be

 x = [ 0 1 1 0 1
       0 0 1 1 1
       1 0 1 1 1 ]

another solution

 x = [ 1 1 0 1 0
       1 1 1 0 0
       1 0 1 1 1 ]

Answer 1

[Walter Roberson]

The solution is the same as

http://www.mathworks.com/matlabcentral/answers/282617-how-to-do-this-operation-on-a-random-matrix#answer_220835

[Firas Al-Kharabsheh]

I need a code to do this , i try to do this but the size of the a random matrix is bigger than G matrix