A group of N players is playing a game. In this game, one player needs to pass the ball to another player.

A player P holds the ball at the start of the game.

A maximum of X moves is allowed to pass the ball so that it ends up with the same player who started the game.

Below is the condition that should be followed by all the players when passing the ball:

A player K$1$can pass the ball to another player K$2$if K$1$divides K$2$or if K$2$divides K$1.$

Your task is to find and return the number of possible ways to complete the game.

Note: A game is considered "complete" if the ball ends up with the player who started it$.$

Input Specification:

Input$1$: An integer value N$,$representing the number of players.

Input$2$: An integer value P$,$representing the player who starts the game.

Input$3$: An integer value X$,$representing the maximum number of moves allowed to pass the ball.

Output Specification:

Return the number of possible ways to complete the game.

Example $1$:

Input$1$: $3$

Input$2$: $2$

Input$3$: $2$

Output: $1$

Explanation:

There are $3$players in the game, and initially the $2$nd player has the ball.

There is a maximum of $2$moves allowed, so the game can be completed in the following way:

$2->1->2.$

Here Player $2$can pass the ball to player $1$as $1$divides $2.$For the same reason,

player $1$can pass the ball to Player $2.$

Since there is only $1$possible way to complete the game, therefore, $1$is returned as the output.

Example $2$:

Input $1$: $3$

Input $2$: $2$

Input $3$: $4$

Output: $3$

Explanation:

There are $3$players in the game, and initially, the $2$nd player has the ball.

There is a maximum of $4$moves allowed, so the game can be completed in the following ways:

$2->1->2$

$2->1->3->1->2$

$2->1->2->1->2$

Therefore, $3$is returned as the output.

do in java and make sure before submitting the solution, try to test the code with the test cases provided.

can you provide the code in java less then $0($n$3)$ complexity