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
Sure, here’s a test case generator for the given problem statement:
### Problem Statement: Determine 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.
**Input:**
Input is given from Standard Input in the following format:
```
N K
```
**Output:**
If we can choose \(K\) integers as above, print `YES`; otherwise, print `NO`.
**Sample Input 1:**
```
13 2
```
**Sample Output 1:**
```
YES
```
**Sample Input 2:**
```
25 5
```
**Sample Output 2:**
```
NO
```
**Sample Input 3:**
```
31 10
```
**Sample Output 3:**
```
YES
```
**Sample Input 4:**
```
10 9
```
**Sample Output 4:**
```
NO
```
### Test Case Generator:
Here’s the code to generate random test cases for this problem:
```python
import random
def tcgen():
N = random.randint(1, 100)
K = random.randint(1, 100)
return N, K
# Example usage:
for _ in range(5):
N, K = tcgen()
print(f"{N} {K}")
```
This code will generate random test cases within the specified constraints. You can run this multiple times to get different sets of \(N\) and \(K\).
Extract Arguments
def extract_arguments(fh):
N, K = map(int, fh.readline().strip().split())
return N, K