Orig Description
Score : 100 points
Problem StatementDetermine if we can choose K different integers between 1 and N (inclusive) so that no two of them differ by 1.
Constraints
1\leq N,K\leq 100
N and K are integers.
InputInput is given from Standard Input in the following format:
N K
OutputIf we can choose K integers as above, print YES; otherwise, print NO.
Sample Input 13 2
Sample Output 1YES
We can choose 1 and 3.
Sample Input 25 5
Sample Output 2NO
Sample Input 331 10
Sample Output 3YES
Sample Input 410 90
Sample Output 4NO
Extracted Specification
Canonicalized Input Description:
An integer N (1 ≤ N ≤ 100), representing some quantity or size.
An integer K (1 ≤ K ≤ 100), representing some quantity or size.
### Example Input:
```
13 2
```
### 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
Certainly! Here is the test case generator for the given problem statement:
```python
import random
def tcgen():
# Constraints
N = random.randint(1, 100)
K = random.randint(1, 100)
return N, K
# Example usage
if __name__ == "__main__":
test_cases = [tcgen() for _ in range(10)]
for i, (N, K) in enumerate(test_cases):
print(f"Sample Input {i+1}")
print(f"{N} {K}")
# Optionally, you can also call the solution function to print the expected output.
# For now, we just print the inputs.
```
This generator will create random test cases for the problem ensuring that values of \(N\) and \(K\) are within the given constraints (1 ≤ \(N, K\) ≤ 100). Each call to `tcgen()` will return a tuple (N, K) representing a test case.
You can run this script and it will generate multiple sample inputs, which you can use to test your solution.
Extract Arguments
def extract_arguments(fh):
N, K = map(int, fh.readline().strip().split())
return N, K