Find the winner of a game of donating i candies in every i-th move

Provided 2 integers X and Y representing the variety of sweets designated to gamers A and B respectively, where both the gamers delight in a video game of contributing i sweets to the challenger in every i ^th relocation. Beginning with gamer A, the video game continues with alternate turns till a gamer is not able to contribute the needed quantity of sweets and loses the video game, the job is to discover the winner of the video game.

Examples:

Input: X = 2, Y = 3
Output: A
Description: The video game ends up in the following way:

Given that A stops working to contribute 5 sweets in the 5 ^th action, B wins the video game.

Input: X = 2, Y = 1
Output: B
Description: The video game ends up in the following way:

Given that B stops working to offer 4 sweets in the 4 ^th action, A wins the video game.

Method: The concept is to resolve the issue based upon the following observation:

Action	Variety of sweets Had by A	Variety of sweets Had by B
0	X	Y
1	X– 1	Y + 1
2	X– 1 + 2 = X + 1	Y + 1– 2 = Y– 1
3	X– 2	Y + 2
4	X + 2	Y– 2

• The gamer whose sweets decrease to 0 initially, will not be having enough sweets to give up the next relocation.
• Count of sweets of gamer A reduces by 1 in odd relocations.
• Count of sweets of gamer B reduces by 1 in even relocations.

Follow the actions listed below to resolve the issue:

1. Initialize 2 variables, state chanceA and chanceB, representing the variety of relocations in which the variety of sweets had by a gamer lowers to 0.
2. Given that count of sweets of gamer A reduces by 1 in odd relocations, chanceA = 2 * (X– 1) + 1
3. Given that count of sweets of gamer B reduces by 1 in even relocations, chanceB = 2 * Y
4. If chanceA < < chanceB, then B will be the winning gamer.
5. Otherwise, A will be the winning gamer.
6. Print the winning gamer.

Below is the execution of the above technique:

Time Intricacy: O( 1 )
Auxiliary Area: O( 1 )

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