Task 1

Let us consider an infinite sequence of stacks indexed from 0, and an exchange operation that removes two tokens from a stack and adds one token to the next stack.

For example, let's assume there are two tokens on stack 0 and three tokens on stack 1. After that operation, there are:

• 2 tokens from stack 0 may be exchanged for one new token on stack 1.
• After that operation, there are four tokens on stack 1 that may be exchanged for two new tokens on stack 2.
• Finally, a new token may be added to stack 3 by exchanging two tokens from stack 2.

This gives us: stacks 0, 1, and 2 empty, and stack 3 with one token.

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Problem Statement

Given the heights of the first N stacks, find the minimum number of tokens that may remain after any number of exchange operations.
You may assume that all of the tokens are identical.
All uninitialized stacks are empty by default.

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Function Signature

class Solution { public int solution(int[] A); }

Parameters

• int A[]: An array of N integers representing the heights of the first N stacks in the sequence.

Returns

• int: The minimum number of tokens which may remain on the stacks after any number of exchange operations.

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Example

Input

A = [2, 3, 0, 0]

Process

1. Stack 0: 2 tokens → exchanged for 1 token in Stack 1.
2. Stack 1: (original 3 + 1 from Stack 0) = 4 tokens → exchanged for 2 tokens in Stack 2.
3. Stack 2: 2 tokens → exchanged for 1 token in Stack 3.

Output

1

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Constraints

• 1 ≤ N ≤ 100,000
• 0 ≤ A[i] ≤ 1,000,000,000

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Task 2

A car manufacturer has data about the production processes of N different cars (numbered from 0 to N-1) and wants to maximize the number of cars produced in the upcoming month.

The manufacturing information is described by an array H, where H[k] denotes the number of hours required to produce the k-th car.

There are two assembly lines in the factory:

• The first assembly line works for X hours in a month.
• The second assembly line works for Y hours in a month.

Each car can be constructed using either one of these lines.
Only one car at a time can be produced on each assembly line, and it is not possible to switch lines after starting the car’s production.

Objective

Find the maximum number of different cars that can be produced in the upcoming month.

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Function Signature

def solution(H, X, Y)

Parameters

• H: an array of N integers representing the time required to produce each car.
• X: an integer, the total available hours of the first assembly line.
• Y: an integer, the total available hours of the second assembly line.

Returns

• An integer: the maximum number of different cars that can be produced.

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Examples

Example 1

H = [1, 1, 3]
X = 1
Y = 1

Output:

2

Explanation:

• Only cars whose assembly time requires 1 hour can be constructed.

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Example 2

H = [6, 5, 5, 4, 3]
X = 8
Y = 9

Output:

4

Explanation:

• The cars that need 3 and 5 hours can be produced on the first assembly line.
• The car that needs 5 hours and the car that needs 4 hours can be produced using the second assembly line.

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Example 3

H = [6, 5, 2, 1, 8, 1]
X = 17
Y = 5

Output:

5

Explanation:

• The car that needs 5 hours can be produced on the second line.
• The four other cars can be produced on the first line.

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Example 4

H = [5, 5, 4, 6]
X = 8
Y = 8

Output:

2

Explanation:

• Only one car can be produced on each line.

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Constraints

• 1 ≤ N ≤ 100,000
• 1 ≤ H[i] ≤ 1,000,000,000
• 1 ≤ X, Y ≤ 1,000,000,000

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