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 PHP (5.6.30) (judge verdict: Accepted)

<?php
error_reporting(0);
$N = trim(fgets(STDIN));
$K = trim(fgets(STDIN));
//$A = explode(" ",trim(fgets(STDIN)));
//list($N,$M) = explode(" ",trim(fgets(STDIN)));

$n=1;
for($i=0;$i<$N;$i++) {
  $wk = $n * 2;
  if ($wk > $K + $n) {
    $n+=$K;
  }
  else {
    $n=$n*2;
  }
}
printf("%d\n",$n);