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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int  N, K;

int calc(vector<int> &V){
  int ans = 1;
  for(int i = 0; i < N; i++){
    if(V[i] == 0) ans *= 2;
    else if(V[i] == 1) ans += K;
  }
  return ans;
}


int dfs(int depth, vector<int> &V){
  if(depth == N) return calc(V);
  else{
    V[depth] = 0;
    int a = dfs(depth + 1, V);
    V[depth] = 1;
    int b = dfs(depth + 1, V);
    return min(a,b);
  }
}

int main(){
  cin >> N >> K;
  
  vector<int> A(N,0);
  //0 := 2* 1:= +K;
  cout << dfs(0, A);
}