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 Go (1.6) (judge verdict: Accepted)

package main

import (
  "fmt"
)

func main() {
  var k, a, b int
  var yen int = 0
  var biscuit uint64 = 1
  fmt.Scan(&k)
  fmt.Scan(&a)
  fmt.Scan(&b)
  if (b - a <= 2) {
    fmt.Println(k + 1)
    return
  }
  for i := 0; i < k; i++ {
    if yen > 0 {
      yen -= 1
      biscuit += uint64(b)
    } else if biscuit >= uint64(a) && i < k - 1 {
      biscuit -= uint64(a)
      yen += 1
    } else {
      biscuit++
    }
  }
  fmt.Println(biscuit)
}