100761: [AtCoder]ABC076 B - Addition and Multiplication
Description
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.