Orig Description
Score : 100 points
Problem StatementTakahashi is distributing N balls to K persons.
If each person has to receive at least one ball, what is the maximum possible difference in the number of balls received between the person with the most balls and the person with the fewest balls?
Constraints
1 \leq K \leq N \leq 100
All values in input are integers.
InputInput is given from Standard Input in the following format:
N K
OutputPrint the maximum possible difference in the number of balls received.
Sample Input 13 2
Sample Output 11
The only way to distribute three balls to two persons so that each of them receives at least one ball is to give one ball to one person and give two balls to the other person.
Thus, the maximum possible difference in the number of balls received is 1.
Sample Input 23 1
Sample Output 20
We have no choice but to give three balls to the only person, in which case the difference in the number of balls received is 0.
Sample Input 38 5
Sample Output 33
For example, if we give 1, 4, 1, 1, 1 balls to the five persons, the number of balls received between the person with the most balls and the person with the fewest balls would be 3, which is the maximum result.
Extracted Specification
An integer \(N\) (1 ≤ \(N\) ≤ 100), representing some quantity.
An integer \(K\) (1 ≤ \(K\) ≤ \(N\)), representing another quantity.
### Example Input:
```
13 2
```
### Function Signature:
Write a function f(N, K) that takes in the input.
```python
def f(N: int, K: int):
'''
N: an integer
K: an integer
'''
```
Test Case Generator
Certainly! Below is the test case generator for the given problem statement:
```python
import random
def tcgen():
N = random.randint(1, 100)
K = random.randint(1, N)
return N, K
# Example usage:
if __name__ == "__main__":
for _ in range(10): # Generate 10 test cases as an example
N, K = tcgen()
print(f"{N} {K}")
```
### Explanation
- **N**: The number of balls is chosen randomly between 1 and 100 inclusive.
- **K**: The number of persons is chosen randomly between 1 and \(N\) inclusive.
This setup ensures that the constraints \(1 \leq K \leq N \leq 100\) are satisfied.
### How to Use
To use this test case generator, simply run the script. Each call to `tcgen()` will generate a new test case with values for \(N\) and \(K\) that can be used to test the solution for the given problem statement.
### Sample Output
Here is how the output might look when generating 10 test cases:
```
67 35
32 20
100 78
45 12
12 5
90 53
1 1
25 10
88 88
50 30
```
Each pair of numbers represents a test case with \(N\) balls and \(K\) persons.
Extract Arguments
def extract_arguments(fh):
N, K = map(int, fh.readline().strip().split())
return N, K