B. ICPC Square
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

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.

Examples
Input
64 35 3
Output
60
Input
2024 2023 1273
Output
1273
Note

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 $$$60 - 30 \leq 35$$$.