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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

"use strict";
function Main(input) {
    let nums = input.split(/\s/).map((v) => v - 0);
    let k = BigInt(nums[0]);
    const a = BigInt(nums[1]);
    const b = BigInt(nums[2]);

    let bs = 1n + k;
    if (a < b && k >= a - 1n) {
        let t = (k - (a - 1n)) / 2n;
        bs = 1n + (k - t * 2n) + (b - a) * t;
    } 
    console.log(bs.toString());
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));