ICPC Square is a hotel provided by the ICPC Committee for the accommodation of the participants. It consists of $N$ floors (numbered from $1$ to $N$). This hotel has a very unique elevator. If a person is currently at floor $x$, by riding the elevator once, they can go to floor $y$ if and only if $y$ is a multiple of $x$ and $y - x \leq D$.

You are currently at floor $S$. You want to go to the highest possible floor by riding the elevator zero or more times. Determine the highest floor you can reach.

Input

A single line consisting of three integers $N$ $D$ $S$ ($2 \leq N \leq 10^{12}; 1 \leq D \leq N - 1; 1 \leq S \leq N$).

Output

Output a single integer representing the highest floor you can reach by riding the elevator zero or more times.

见题面 Input 部分

见题面 Output 部分

Explanation for the sample input/output #1

First, ride the elevator from floor $3$ to floor $15$. This is possible because $15$ is a multiple of $3$ and $15 - 3 \leq 35$. Then, ride the elevator from floor $15$ to floor $30$. This is possible because $30$ is a multiple of $15$ and $30 - 15 \leq 35$. Finally, ride the elevator from floor $30$ to floor $60$. This is possible because $60$ is a multiple of $30$ and $60 - 30 \leq 35$.