There are n players sitting in a circle. The game starts from player i, and a value k is given.

In each round, players are counted in the circular manner, and the player at position i + k is eliminated. After eliminating a player, the counting continues from the next remaining player.

This process continues until the required number of rounds is completed.

Your task is to determine how many players are eliminated after k rounds.

Input

• The first line contains an integer n — the number of players.

• The second line contains two integers i and k:

  • i — the starting player.
  • k — the number of rounds.

Output

Print the number of players eliminated after k rounds.

Constraints

1 ≤ n ≤ 10^9
1 ≤ i ≤ n
1 ≤ k ≤ n

Example

Input:
10
2 3

Output:
3

Explanation

There are 10 players arranged in a circle. The game starts from player 2.

In every round, counting continues circularly and the player at the required i + k position is eliminated.

After 3 rounds, 3 players have been eliminated.