Cake cuts

You are presented with a rectangular cake whose sides are of length X and Y.
The cake has been cut into (N + 1) pieces by making N
 straight cuts along the first side and N straight cuts along the second side.

The cuts are represented by two non-empty zero-indexed arrays A and B
 consisting of N integers. More precisely, A[i] such that 0 ≤ i < N
 represents the position of a cut along the first side, and B[j] such that
 0 ≤ j < N represents the position of a cut along the second side.
We could also make a different number of cuts on the second side but for now the number of cuts is equal on both sides.

The goal is to find the K-th piece of cake in order of size, starting with
 the largest piece first. We will consider the size of a piece to be its area.

N is an integer within the range [1..40,000];
X and Y are integers within the range [2..400,000,000];
K is an integer within the range [1..(N+1)*(N+1)];
each element of array A is an integer within the range [1..X−1];
each element of array B is an integer within the range [1..Y−1];
A[i − 1] < A[i] and B[i − 1] < B[i], for every i such that 0 < i< N;
1 ≤ A[i] − A[i − 1], B[i] − B[i − 1] ≤ 10,000, for every i such that 0 < i < N;
1 ≤ A[0], B[0], X − A[N − 1], Y − B[N − 1] ≤ 10,000

   - first the biggest piece is searched, then the second biggest piece .. all is done K times, and when the K iteration is reached, the size of the biggest piece of cake that was found, is returned