Use values of array as indices for different array

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I have two matrices, A, B, and C, shown below:

A =  [16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1];
 
B = [1    3
    2    3
    1    4];
C = [1 3 4];

I want to use the elements of B and C as indices of A to create a new matrix, D, such that each element in C corresponds to a row index in A, and the values in each row of B correspond to column indices given the row index from C. e.g. C(1) = 1 and B(1,:) = [1 3] gives me D(1,:) = A(1,[1 3]). The resulting matrix D would look as follows:

D = [16    3
    7    6
    4    1];

This is relatively straightforward with a for-loop, but I was hoping for a one-line solution along the lines of A(C,B) = D, which doesn't do what I'm describing in MATLAB. Does anything like what I'm describing exist?