Problem:
Score : 400 points

Problem Statement

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket.
He will perform the following operations exactly K times in total, in the order he likes:

Hit his pocket, which magically increases the number of biscuits by one.

Exchange A biscuits to 1 yen.

Exchange 1 yen to B biscuits.

Find the maximum possible number of biscuits in Snuke's pocket after K operations.

Constraints

1 \leq K,A,B \leq 10^9

K,A and B are integers.

Input

Input is given from Standard Input in the following format:

K A B

Output

Print the maximum possible number of biscuits in Snuke's pocket after K operations.

Sample Input 1

4 2 6

Sample Output 1

7

The number of biscuits in Snuke's pocket after K operations is maximized as follows:

Hit his pocket. Now he has 2 biscuits and 0 yen.

Exchange 2 biscuits to 1 yen. his pocket. Now he has 0 biscuits and 1 yen.

Hit his pocket. Now he has 1 biscuits and 1 yen.

Exchange 1 yen to 6 biscuits. his pocket. Now he has 7 biscuits and 0 yen.

Sample Input 2

7 3 4

Sample Output 2

8

Sample Input 3

314159265 35897932 384626433

Sample Output 3

48518828981938099

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class Main
{
    public static void main(String[] args)throws IOException {
        BufferedReader bufferedReader=new BufferedReader(new InputStreamReader(System.in));
        String[]s=bufferedReader.readLine().split( " ");
        long k=Long.parseLong(s[0]),a=Long.parseLong(s[1]),b=Long.parseLong(s[2]);
        List<Long>list=new ArrayList<>();
        list.add(k+1);
        k-=((a-1)+2);
        long ans = 0;
        if(k==0)
            ans=b;
        if(k>0 && b>a) {
            ans = b;
            while (k > 1) {
                ans -= a;
                ans += b;
                k-=2;
            }
        }
        if(k==1)
            ans++;
        list.add(ans);
        System.out.println(Collections.max(list));
    }
}