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:**↵
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.
↵
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
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.
