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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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

^{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.

Assume that:

- 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.

Complexity:

- expected worst-case time complexity is O(N*log(N+X+Y));

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