Orig Description
Score : 200 points
Problem StatementSquare1001 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.
InputInput is given from Standard Input in the following format:
N
K
OutputPrint the minimum possible value displayed in the board after N operations.
Sample Input 14
3
Sample Output 110
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 210
10
Sample Output 276
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.
Extracted Specification
An integer N (1 ≤ N ≤ 10), representing some quantity or size.
An integer K (1 ≤ K ≤ 10).
### Example Input:
```
3
10
```
### Function Signature:
Write a function f(N, K) that takes in the input.
def f(N: int, K: int):
'''
N: an integer
K: an integer
'''
Test Case Generator
Sure! The task is to create a test case generator for the problem where we need to find the minimum possible value displayed on the board after a series of operations. Below is a Python function that generates random test cases for this problem:
```python
import random
def tcgen():
N = random.randint(1, 10) # N is between 1 and 10 inclusive
K = random.randint(1, 10) # K is between 1 and 10 inclusive
return N, K
# Example of generating and printing a test case
N, K = tcgen()
print(N)
print(K)
```
### Explanation
- `N` represents the number of operations to be performed and can be any integer between 1 and 10 inclusive.
- `K` represents the value by which the number on the board increases when operation B is performed and can be any integer between 1 and 10 inclusive.
This function will generate random values for `N` and `K` within the specified constraints. You can call this function to generate test cases for your problem.
### Example Output
Here are some example outputs you might get from running the `tcgen` function:
```
3
7
```
```
10
2
```
You can use these random generated test cases to test your solution to the problem.