Tower Breakers | HackerRank

Two players are playing a game of Tower Breakers! Player always moves first, and both players always play optimally.The rules of the game are as follows:

Initially there are towers.
Each tower is of height .
The players move in alternating turns.
In each turn, a player can choose a tower of height and reduce its height to , where and evenly divides .
If the current player is unable to make a move, they lose the game.

Given the values of and , determine which player will win. If the first player wins, return . Otherwise, return .

Example.

There are towers, each units tall. Player has a choice of two moves:
- remove pieces from a tower to leave as
- remove pieces to leave

Let Player remove . Now the towers are and units tall.

Player matches the move. Now the towers are both units tall.

Now Player has only one move.

Player removes pieces leaving . Towers are and units tall.
Player matches again. Towers are both unit tall.

Player has no move and loses. Return .

Function Description

Complete the towerBreakers function in the editor below.

towerBreakers has the following paramter(s):

int n: the number of towers
int m: the height of each tower

Returns

int: the winner of the game

Input Format

The first line contains a single integer , the number of test cases.
Each of the next lines describes a test case in the form of space-separated integers, and .

Constraints

Sample Input

STDIN   Function
-----   --------
2       t = 2
2 2     n = 2, m = 2
1 4     n = 1, m = 4

Sample Output

2
1

Explanation

We'll refer to player as and player as

In the first test case, chooses one of the two towers and reduces it to . Then reduces the remaining tower to a height of . As both towers now have height , cannot make a move so is the winner.

In the second test case, there is only one tower of height . can reduce it to a height of either or . chooses as both players always choose optimally. Because has no possible move, wins.