Problem Brief

Get Optimal String Length

FULLTIMEOA

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A string is to be constructed using only the characters 'A' and 'B'. Given four integers, countA, countB, maxA, maxB, the constructed string is said to be optimal if:

There are at most countA 'A' characters, and countB 'B' characters.

Each substring of only 'A's contains at most maxA 'A' characters.

Each substring of only 'B's contains at most maxB 'B' characters.

HackerRank organized fun trivia for its employees where it asked for the maximum possible length of an optimal string that can be constructed satisfying the criteria above. The goal is to find the maximum possible length of an optimal string.

Note:

There can be multiple optimal strings with the same maximal length.
A substring of a string is a contiguous subsegment of the string.

Function Description

Complete the function getOptimalStringLength in the editor.

getOptimalStringLength has the following parameters:

int countA: the maximum count of character 'A'
int countB: the maximum count of character 'B'
int maxA: the maximum substring length of character 'A'
int maxB: the maximum substring length of character 'B'

Returns

long integer: the maximum length of optimal string that can be constructed

1Example 1

Input

countA = 3, countB = 5, maxA = 1, maxB = 1

Output

Explanation

The maximal length optimal string that can be constructed is 'BABABAB' whose length is 7. Thus, the answer is 7.

2Example 2

Input

countA = 2, countB = 4, maxA = 2, maxB = 1

Output

Explanation

The maximal length optimal string is 'ABABA'.

Constraints

Limits and guarantees your solution can rely on.

0 ≤ countA, countB, maxA, maxB ≤ 10⁶