Problem p01939 - Generation 2

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

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

### Example Input:

```
3 9
```

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

Test Case Generator

Sure, I can help you write a test case generator for the provided problem statement. Given the constraints, especially the very large bounds for `n` and `m`, our generator will produce values within these bounds, but we should be mindful of the potential computational challenges involved in generating very large numbers.

Here's a Python function to generate test cases for the problem statement "Ebi-chan and Integer Sequences":

```python
import random

def tcgen():
    # Define the modulo constant
    MOD = 10**9 + 7
    
    # Generate a random value for n within the specified bounds
    n = random.randint(1, 10**15)
    
    # Generate a random value for m within the specified bounds
    m = random.randint(0, 10**15)
    
    return n, m

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

This function will generate a random pair `(n, m)` where `1 ≤ n ≤ 10^15` and `0 ≤ m ≤ 10^15`. Note that due to the large range of possible values, the integers generated can be very large, and the output may not fit in standard 32-bit integers.

Please keep in mind that handling such large numbers might require efficient algorithms and data structures, especially given the constraints of competitive programming environments.

Extract Arguments

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

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