Problem p01939 - Generation 1

Orig Description

B: Ebi-chan and Integer Sequences -
Problem
Ebi-chan likes integer sequences, especially arithmetic sequences.
This time, she decided to create a sequence that satisfies the following conditions:
It is an arithmetic sequence of length n.
When the i-th element of the sequence is denoted by s_i, all s_i (1 \leq i \leq n) are integers satisfying 0 \leq s_i \leq m.
How many arithmetic sequences can be created that satisfy the above conditions?
Since the answer can be very large, output it modulo 10^9 + 7.
Input Format
The input is given in a single line.
n m
n represents the length of the sequence.
Constraints
1 \leq n \leq 10^{15}
0 \leq m \leq 10^{15}
Output Format
Output the number of arithmetic sequences that satisfy the above conditions, modulo 10^9 + 7.
Sample Input 1
3 9
Sample Output 1
50
Sample Input 2
10000000000 10000000000
Sample Output 2
999999942
Note that the input may not fit in a 32-bit integer.

Extracted Specification

### Canonicalized Input Description:

An integer n (1 ≤ n ≤ 10^15), representing some quantity or size.
An integer m (0 ≤ m ≤ 10^15), representing some quantity or size.

### Example Input:

```
3 9
```

### Function Signature:
Write a function f(n, m) that takes in the input.
```python
def f(n: int, m: int):
    '''
    n: an integer
    m: an integer
    '''
```

Test Case Generator

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

```python
import random

def tcgen():
    # Define the constraints
    max_n = 10**15
    max_m = 10**15
    
    # Generate random values for n and m within the constraints
    n = random.randint(1, max_n)
    m = random.randint(0, max_m)
    
    return n, m

# Example usage of the test case generator
if __name__ == "__main__":
    n, m = tcgen()
    print(f"{n} {m}")
```

Explanation:
- The generator function `tcgen` creates random test cases within the specified constraints.
- `n` is generated randomly between 1 and \(10^{15}\).
- `m` is generated randomly between 0 and \(10^{15}\).
- The function returns a tuple `(n, m)`.
- The example usage at the end is for demonstration purposes, printing the generated test case in the format expected by the problem.

Since `n` and `m` can be very large and may not fit in a 32-bit integer, Python's `int` type, which can handle arbitrarily large integers, is used.

Extract Arguments

def extract_arguments(fh):
    n, m = map(int, fh.readline().strip().split())
    return n, m