Orig Description
Score : 600 points
Problem StatementGiven are two strings s and t consisting of lowercase English letters. Determine if the number of non-negative integers i satisfying the following condition is finite, and find the maximum value of such i if the number is finite.
There exists a non-negative integer j such that the concatenation of i copies of t is a substring of the concatenation of j copies of s.
Notes
A string a is a substring of another string b if and only if there exists an integer x (0 \leq x \leq |b| - |a|) such that, for any y (1 \leq y \leq |a|), a_y = b_{x+y} holds.
We assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings s and t, i = 0 satisfies the condition in the problem statement.
Constraints
1 \leq |s| \leq 5 \times 10^5
1 \leq |t| \leq 5 \times 10^5
s and t consist of lowercase English letters.
InputInput is given from Standard Input in the following format:
s
t
OutputIf the number of non-negative integers i satisfying the following condition is finite, print the maximum value of such i; if the number is infinite, print -1.
Sample Input 1abcabab
ab
Sample Output 13
The concatenation of three copies of t, ababab, is a substring of the concatenation of two copies of s, abcabababcabab, so i = 3 satisfies the condition.
On the other hand, the concatenation of four copies of t, abababab, is not a substring of the concatenation of any number of copies of s, so i = 4 does not satisfy the condition.
Similarly, any integer greater than 4 does not satisfy the condition, either. Thus, the number of non-negative integers i satisfying the condition is finite, and the maximum value of such i is 3.
Sample Input 2aa
aaaaaaa
Sample Output 2-1
For any non-negative integer i, the concatenation of i copies of t is a substring of the concatenation of 4i copies of s. Thus, there are infinitely many non-negative integers i that satisfy the condition.
Sample Input 3aba
baaab
Sample Output 30
As stated in Notes, i = 0 always satisfies the condition.
Extracted Specification
Canonicalized Input Description:
A string s consisting of lowercase English letters with length between 1 and 500,000.
A string t consisting of lowercase English letters with length between 1 and 500,000.
### Example Input:
```
abcabab
ab
```
### Function Signature:
Write a function f(s, t) that takes in the input.
```python
def f(s: str, t: str):
'''
s: a string
t: a string
'''
```
Test Case Generator
Sure, here is the test case generator for the given problem statement:
```python
import random
import string
def generate_string(length):
return ''.join(random.choices(string.ascii_lowercase, k=length))
def tcgen():
# Generate length of strings s and t within the given constraints
len_s = random.randint(1, 5 * 10**5)
len_t = random.randint(1, 5 * 10**5)
# Generate random strings s and t of the generated lengths
s = generate_string(len_s)
t = generate_string(len_t)
return s, t
# Example usage
if __name__ == "__main__":
s, t = tcgen()
print(s)
print(t)
```
### Explanation
1. **generate_string(length):** This helper function generates a random string of a given length using lowercase English letters.
2. **tcgen():** The main function that generates test cases.
- It first generates random lengths for strings `s` and `t` within the given constraints (1 to 5 * 10^5).
- It then generates random strings `s` and `t` of the given lengths.
- It returns the generated strings `s` and `t`.
### Usage
The script includes an example usage of the `tcgen` function, which prints out a pair of randomly generated strings that can be used as test cases for the problem. This ensures that the test cases adhere to the constraints specified in the problem statement.