Problem p04035 - Generation 2

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

Canonicalized Input Description:

An integer N (2 ≤ N ≤ 10^5), representing some quantity or size.
An integer L (1 ≤ L ≤ 10^9), representing another quantity.
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

Certainly! Here is a test case generator for the given problem statement:

```python
import random

def tcgen():
    N = random.randint(2, 10**5)
    L = random.randint(1, 10**9)
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, L, A

# Example usage:
N, L, A = tcgen()
print(N)
print(L)
print(" ".join(map(str, A)))
```

This code will generate a random test case for the problem by following these steps:
1. Randomly choose the number of ropes \( N \) between 2 and \( 10^5 \).
2. Randomly choose the minimum length \( L \) between 1 and \( 10^9 \).
3. Generate a list \( A \) of \( N \) integers, each between 1 and \( 10^9 \), representing the lengths of the ropes.

You can run the `tcgen` function to get randomized inputs for testing purposes in competitive programming.

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

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#     N, L, A = extract_arguments(fh)
#     f(N, L, A)