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Find the K-th piece of a cake in terms of size.

Programming language:
Spoken language:

You are presented with a rectangular cake whose sides are of length X and Y. The cake has been cut into (N + 1)^{2} 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 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[I] such that 0 ≤ I < N represents the position of a cut along the second side.

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.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

There are nine pieces of cake, and their consecutive sizes are: 12, 8, 6, 4, 4, 3, 2, 2, 1. In the figure above, the third piece of cake is highlighted; its size equals 6.

Write a function:

int solution(int X, int Y, int K, int A[], int B[], int N);

that, given three integers X, Y, K and two non-empty arrays A and B of N integers, returns the size of the K-th piece of cake.

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

You are presented with a rectangular cake whose sides are of length X and Y. The cake has been cut into (N + 1)^{2} 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 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[I] such that 0 ≤ I < N represents the position of a cut along the second side.

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.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

There are nine pieces of cake, and their consecutive sizes are: 12, 8, 6, 4, 4, 3, 2, 2, 1. In the figure above, the third piece of cake is highlighted; its size equals 6.

Write a function:

int solution(int X, int Y, int K, vector<int> &A, vector<int> &B);

that, given three integers X, Y, K and two non-empty arrays A and B of N integers, returns the size of the K-th piece of cake.

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

You are presented with a rectangular cake whose sides are of length X and Y. The cake has been cut into (N + 1)^{2} 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 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[I] such that 0 ≤ I < N represents the position of a cut along the second side.

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.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

There are nine pieces of cake, and their consecutive sizes are: 12, 8, 6, 4, 4, 3, 2, 2, 1. In the figure above, the third piece of cake is highlighted; its size equals 6.

Write a function:

class Solution { public int solution(int X, int Y, int K, int[] A, int[] B); }

that, given three integers X, Y, K and two non-empty arrays A and B of N integers, returns the size of the K-th piece of cake.

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

func Solution(X int, Y int, K int, A []int, B []int) int

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

class Solution { public int solution(int X, int Y, int K, int[] A, int[] B); }

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

function solution(X, Y, K, A, B);

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

function solution(X, Y, K, A, B)

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

Note: All arrays in this task are zero-indexed, unlike the common Lua convention. You can use `#A` to get the length of the array A.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

int solution(int X, int Y, int K, NSMutableArray *A, NSMutableArray *B);

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

function solution(X: longint; Y: longint; K: longint; A: array of longint; B: array of longint; N: longint): longint;

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

function solution($X, $Y, $K, $A, $B);

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

sub solution { my ($X, $Y, $K, $A, $B)=@_; my @A=@$A; my @B=@$B; ... }

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

def solution(X, Y, K, A, B)

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

def solution(x, y, k, a, b)

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

object Solution { def solution(x: Int, y: Int, k: Int, a: Array[Int], b: Array[Int]): Int }

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

public func solution(X : Int, _ Y : Int, _ K : Int, inout _ A : [Int], inout _ B : [Int]) -> Int

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

public func solution(_ X : Int, _ Y : Int, _ K : Int, _ A : inout [Int], _ B : inout [Int]) -> Int

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

^{2} pieces by making N straight cuts along the first side and N straight cuts along the second side.

For example, a cake with sides X = 6, Y = 7 and arrays A and B such that:

is represented by the figure below.

Write a function:

Private Function solution(X As Integer, Y As Integer, K As Integer, A As Integer(), B As Integer()) As Integer

For example, given:

the function should return 6, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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.

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