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 (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func swap(a int64, b int64) (int64, int64) {
	return b, a
}

func gcd(a int64, b int64) int64 {
	if b > a {
		a, b = swap(a, b)
	}
	if b == 0 {
		return a
	} else {
		return gcd(a%b, b)
	}
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func min(nums ...int64) int64 {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int64(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int64) int64 {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int64(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func nextLong() int64 {
	sc.Scan()
	i, e := strconv.ParseInt(sc.Text(), 10, 64)
	if e != nil {
		panic(e)
	}
	return i
}

func nextString() string {
	sc.Scan()
	s := sc.Text()
	return s
}

func nextByte() byte {
	sc.Scan()
	s := sc.Bytes()
	return s[0]
}

func main() {
	sc.Split(bufio.ScanWords)
	//ans := 1
	K := nextLong()
	A := nextLong()
	B := nextLong()
	ans := int64(0)
	if A >= B || (B-A) == 1 {
		ans = 1 + K
	} else {
		K -= (A - int64(1))
		if K%int64(2) == 0 {
			ans = A + (B-A)*(K/int64(2))
		} else {
			ans = A + (B-A)*(K/int64(2))
			ans += int64(1)
		}
	}

	fmt.Printf("%d\n", ans)
}