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)