Fill array with elements located at specified subscripts in another array

I have a 3D array, A, of size IxJxK as well as a list of N 2D coordinates in an array I (see below). I want to fill a 2D array, B, of size KxN with the elements of A as indicated in the comments in the code below.

Asize = [128,128,64];
A = rand(Asize(1),Asize(2),Asize(3));
N = 1e+3;
[Ir,Ic] = ind2sub(Asize,randperm(prod(Asize(1:2)),N));
I = [Ir',Ic'];

B = zeros(Asize(3),N);
% B(:,n) should contain the elements A(I(n,1),I(n,2),:)

Is there a fast way to do this that does not involve loops?

Answer 1

[Matt J]

 Ap=reshape( permute(A,[3,1,2])  , Asize(3),[] );

 B=Ap(:, randperm(prod(Asize(1:2)),N)  ).' ;

[Aaron J. Hendrickson]

That works. One edit though: Just need to remove the .' in the second line. Thanks!