Problem Statement

You are given three integers ~n~, ~x~ and ~k~.

You have the following infinite sequence \(S = [1 \small\text{ mod } \normalsize k,\ \ \ (1 + 2) \small\text{ mod }\normalsize k,\ \ \ (1 + 2 + 3) \small\text{ mod }\normalsize k,\ ... ]\), in other words \(S_i = (\sum_{j=1}^ij) \small\text{ mod }\normalsize k\).

Determine at which index (one-indexed) the ~n^{th}~ occurrence of ~x~ is in the sequence ~S~ if ~x~ occurs at least ~n~ times, otherwise output ~-1~.

Input Format

Your first line will contain three space-separated integers ~n~, ~x~ and ~k~ respectively.

Output Format

You should output a single integer, representing the index (one-indexed) in ~S~ at which the ~n^{th}~ occurrence of ~x~ appears. If it does not appear at least ~n~ times, then output ~-1~.

Constraints

• ~1 \leq n \leq 10^{9}~
• ~1 \leq k \leq 10^2~
• ~0 \leq x < k~

Sample Cases

Input 1

1 1 10

Output 1

1

Input 2

2 1 10

Output 2

6

Input 3

20 2 13

Output 3

124

Input 4

20 2 10

Output 4

-1

Template

n, x, k = map(int, input().split())

# print your output