So I am kind of stuck in a problem related to game theory!↵
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Any help will be appreciated!↵
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**Problem:**↵
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Anjali and Vaibhavi are playing a game with a pile of N coins. In this game, Anjali and Vaibhavi make their respective moves ↵
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alternately, starting with Anjali.↵
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In a turn, a player can remove x coins from the pile if x satisfies: 1<= x <= n↵
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x & n = 0 (bitwise and of x and n is 0.)↵
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where 'n' is the size of the pile in the current turn.↵
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The player who is unable to make a move loses the game.↵
↵
Given the initial number of coins in a pile, determine who would win the game.↵
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Assume that both the players play optimally throughout the game.↵
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**Input Format:**↵
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First-line denotes t i.e. number of test cases↵
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Next ‘t’ lines contain n where n is the number of coins in the pile as the game commences.↵
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**Output Format:**↵
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For each test case, print the winning player’s name (case sensitive).↵
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**Constraints:**↵
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1 <= t <= 10^5↵
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1 <= n <= 10^18↵
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**Sample Input:**↵
↵
5↵
↵
1↵
↵
2↵
↵
3 ↵
↵
4↵
↵
5↵
↵
**Sample Output:**↵
↵
Vaibhavi↵
↵
Anjali↵
↵
Vaibhavi↵
↵
Anjali↵
↵
Anjali↵
↵
**Explanation:**↵
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1st test case: Anjali can't make a move so Vaibhavi wins.↵
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2nd test case: Anjali can remove 1 coin because 1&2=0 then 1 coin left so Vaibhavi can't make a move so Anjali wins.↵
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3rd test case: Anjali can't make a move, so Vaibhavi wins.↵
↵
And so on.
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Any help will be appreciated!↵
↵
**Problem:**↵
↵
Anjali and Vaibhavi are playing a game with a pile of N coins. In this game, Anjali and Vaibhavi make their respective moves ↵
↵
alternately, starting with Anjali.↵
↵
In a turn, a player can remove x coins from the pile if x satisfies: 1<= x <= n↵
↵
x & n = 0 (bitwise and of x and n is 0.)↵
↵
where 'n' is the size of the pile in the current turn.↵
↵
The player who is unable to make a move loses the game.↵
↵
Given the initial number of coins in a pile, determine who would win the game.↵
↵
Assume that both the players play optimally throughout the game.↵
↵
**Input Format:**↵
↵
First-line denotes t i.e. number of test cases↵
↵
Next ‘t’ lines contain n where n is the number of coins in the pile as the game commences.↵
↵
**Output Format:**↵
↵
For each test case, print the winning player’s name (case sensitive).↵
↵
**Constraints:**↵
↵
1 <= t <= 10^5↵
↵
1 <= n <= 10^18↵
↵
**Sample Input:**↵
↵
5↵
↵
1↵
↵
2↵
↵
3 ↵
↵
4↵
↵
5↵
↵
**Sample Output:**↵
↵
Vaibhavi↵
↵
Anjali↵
↵
Vaibhavi↵
↵
Anjali↵
↵
Anjali↵
↵
**Explanation:**↵
↵
1st test case: Anjali can't make a move so Vaibhavi wins.↵
↵
2nd test case: Anjali can remove 1 coin because 1&2=0 then 1 coin left so Vaibhavi can't make a move so Anjali wins.↵
↵
3rd test case: Anjali can't make a move, so Vaibhavi wins.↵
↵
And so on.
