Problem:
Score : 200 points

Problem Statement

Square1001 has seen an electric bulletin board displaying the integer 1.
He can perform the following operations A and B to change this value:

Operation A: The displayed value is doubled.

Operation B: The displayed value increases by K.

Square1001 needs to perform these operations N times in total.
Find the minimum possible value displayed in the board after N operations.

Constraints

1 \leq N, K \leq 10

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the minimum possible value displayed in the board after N operations.

Sample Input 1

4
3

Sample Output 1

10

The value will be minimized when the operations are performed in the following order: A, A, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.

Sample Input 2

10
10

Sample Output 2

76

The value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76.

By the way, this contest is AtCoder Beginner Contest 076.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int K = Integer.parseInt(sc.next());
        sc.close();

        int ans = 0;

        if (K == 1) {

            System.out.println(1+N);
        } else if (K > 1 && K <= 3) {

            if ( N > 2) {

                ans = 4 + K*(N-2);
            } else {

                ans = (int) Math.pow(2,N);
            }

            System.out.println(ans);
        } else if (K > 3 && K <= 7) {

            if ( N > 3) {

                ans = 8 + K*(N-3);
            } else {

                ans = (int) Math.pow(2,N);
            }
            System.out.println(ans);
        } else {

            if ( N > 4) {

                ans = 16 + K*(N-4);
            } else {

                ans = (int) Math.pow(2,N);
            }
            System.out.println(ans);
        }
    }

}