Orig Description
Score : 300 points
Problem StatementThe problem set at CODE FESTIVAL 20XX Finals consists of N problems.
The score allocated to the i-th (1≦i≦N) problem is i points.
Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.
As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.
Determine the set of problems that should be solved.
Constraints
1≦N≦10^7
Partial Score
200 points will be awarded for passing the test set satisfying 1≦N≦1000.
Additional 100 points will be awarded for passing the test set without additional constraints.
InputThe input is given from Standard Input in the following format:
N
OutputAmong the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.
If there exists more than one such set, any of them will be accepted.
Sample Input 14
Sample Output 11
3
Solving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.
Sample Input 27
Sample Output 21
2
4
The set \{3,4\} will also be accepted.
Sample Input 31
Sample Output 31
Extracted Specification
An integer N (1 ≤ N ≤ 10^7).
### Example Input:
```
7
```
### Function Signature:
Write a function f(N) that takes in the input.
def f(N: int):
'''
N: an integer
'''
Test Case Generator
Sure, let's write a test case generator for the given problem statement. Here is the generator function:
```python
import random
def tcgen():
# Generate a random value for N within the constraints
N = random.randint(1, 10**7)
return N
# Example usage
print(tcgen())
```
This generator function will produce a random test case for the given problem where \(N\) is a single integer within the range \([1, 10^7]\).
Since the problem requires only a single integer \(N\) as input, the generator function is straightforward. You can call this function to generate random test cases for testing your solution to the problem.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
return (N,)