Problem p04035 - Generation 3

Orig Description

Problem StatementWe have N pieces of ropes, numbered 1 through N. The length of piece i is a_i.
At first, for each i (1≤i≤N-1), piece i and piece i+1 are tied at the ends, forming one long rope with N-1 knots. Snuke will try to untie all of the knots by performing the following operation repeatedly:
Choose a (connected) rope with a total length of at least L, then untie one of its knots.
Is it possible to untie all of the N-1 knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots.
Constraints
2≤N≤10^5
1≤L≤10^9
1≤a_i≤10^9
All input values are integers.
InputThe input is given from Standard Input in the following format:
N L
a_1 a_2 ... a_n
OutputIf it is not possible to untie all of the N-1 knots, print Impossible.
If it is possible to untie all of the knots, print Possible, then print another N-1 lines that describe a possible order to untie the knots. The j-th of those N-1 lines should contain the index of the knot that is untied in the j-th operation. Here, the index of the knot connecting piece i and piece i+1 is i.
If there is more than one solution, output any.
Sample Input 13 50
30 20 10
Sample Output 1Possible
2
1
If the knot 1 is untied first, the knot 2 will become impossible to untie.
Sample Input 22 21
10 10
Sample Output 2Impossible
Sample Input 35 50
10 20 30 40 50
Sample Output 3Possible
1
2
3
4
Another example of a possible solution is 3, 4, 1, 2.

Extracted Specification

An integer N (2 ≤ N ≤ 10^5), representing some quantity or size.
An integer L (1 ≤ L ≤ 10^9), representing some threshold.
A list of integers A of size N, where each integer is between 1 and 10^9.

### Example Input:
```
3 50
30 20 10
```

### Function Signature:
Write a function f(N, L, A) that takes in the input.
```python
def f(N: int, L: int, A: List[int]):
    '''
    N: an integer
    L: an integer
    A: a list of integers
    '''
```

Test Case Generator

Sure, I can help you create a test case generator for the given problem statement. Below is the Python code for the test case generator:

```python
import random

def tcgen():
    # Define constraints
    N = random.randint(2, 10**5)
    L = random.randint(1, 10**9)
    
    # Generate the lengths of the ropes
    a = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, L, a

# Example usage
for _ in range(5):  # Generate 5 test cases
    N, L, a = tcgen()
    print(f"Input:")
    print(f"{N} {L}")
    print(" ".join(map(str, a)))
    print()
```

This code snippet generates random test cases for the problem. Here is a breakdown of the code:

1. **Define Constraints**: The number of ropes \( N \) is randomly chosen between 2 and \( 10^5 \). The minimum length \( L \) is randomly chosen between 1 and \( 10^9 \).

2. **Generate Lengths of the Ropes**: The lengths of the ropes are generated as a list \( a \) with \( N \) elements, each randomly chosen between 1 and \( 10^9 \).

3. **Return the Generated Test Case**: The function returns the values of \( N \), \( L \), and \( a \).

4. **Example Usage**: The example at the end demonstrates how to use the `tcgen` function to generate and print 5 test cases.

You can run this script to generate as many test cases as you need for the problem.

Extract Arguments

def extract_arguments(fh):
    N, L = map(int, fh.readline().strip().split())
    A = list(map(int, fh.readline().strip().split()))
    return N, L, A