Compare vector to matrix of unique dimensions

I have a column vector (5000x1) and a matrix (5x3). I want to find the maximum index (ii = 1,2,3) for each element of the vector against each row of the matrix where the vector element is less than or equal to the indexed element. I will end up with a matrix of size (5000x5). If the vector element is greater than all elements in a row, return 3 as the index.

Example with a (6x1) vector and (5x3) matrix:

v = [1 1 2 1 2 3]'; A = [0 1 2
                         1 2 3
                         0 0 0
                         1 1 2
                         2 3 4];

Output (6x5): B = [2 1 3 1 1 
                   2 1 3 1 1
                   3 2 3 3 1
                   2 1 3 1 1
                   3 2 3 3 1
                   3 3 3 3 2];

Answer 1

[xtremecheez]

For anybody looking at this question in the future:

Using permute as Andrei suggested, the following gives the exact answer as desired (though it could be made more elegant).

P = v <= permute(A,[3 1 2]);
[~,out] = max(c,[],3);
out(sum(P,3)==0) = 3;

Answer 2

[Andrei Bobrov]

out = sum(permute(A,[3,1,2]) <= v,3);

[xtremecheez]

I can work with that, thanks. Edit: I unaccepted your answer in favor of my solution that produced exactly what I wanted. You led me there though, hence the upvote.