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: Wrong Answer)

function Main(input) {
	input = input.split(' ');
        var K=parseInt(input[0]);
        var A=parseInt(input[1]);
        var B=parseInt(input[2]);
        var D=B-A;
        var E=K-A;
        var biscuit=0;
if((E<2)||(D<3)){
  biscuit=K+1;
}else if((E+1)%2===1){
  biscuit=(A+E*D/2+1);
}else{
  biscuit=(A+(E+1)*D/2);
}

console.log(biscuit);
}

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