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)

var BigInteger = require("big-integer");
function Main(input) {
  input = input.split("\n");
  var K=parseInt(input[0].split(" ")[0]);
  var A=parseInt(input[0].split(" ")[1]);
  var B=parseInt(input[0].split(" ")[2]);

  var ans=K+1;

  if(B>2+A){
    var N = K-A;
    if(N==1){
      ans=B;
    }else if(N%2==1){
      var X = BigInteger(Math.floor((K-A)/2));
      var Y = BigInteger(B-A);
      var Z = BigInteger(B);
      var XY = X.multiply(Y);
      var XYZ = XY.plus(Z);
      ans = XYZ.toString();
    }else if(N%2==0){
      var X = BigInteger(Math.floor((K-A)/2-1));
      var Y = BigInteger(B-A);
      var Z = BigInteger(B+1);
      var XY = X.multiply(Y);
      var XYZ = XY.plus(Z);
      ans = XYZ.toString();
    }
  }



  console.log('%s', ans);
}
  
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(){
  var input = document.getElementById("input").value;
  Main(input);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));