Problem p02937 - Generation 3

Orig Description

Score : 500 points
Problem StatementGiven are two strings s and t consisting of lowercase English letters. Determine if there exists an integer i satisfying the following condition, and find the minimum such i if it exists.
Let s' be the concatenation of 10^{100} copies of s. t is a subsequence of the string {s'}_1{s'}_2\ldots{s'}_i (the first i characters in s').
Notes
A subsequence of a string a is a string obtained by deleting zero or more characters from a and concatenating the remaining characters without changing the relative order. For example, the subsequences of contest include net, c, and contest.
Constraints
1 \leq |s| \leq 10^5
1 \leq |t| \leq 10^5
s and t consists of lowercase English letters.
InputInput is given from Standard Input in the following format:
s
t
OutputIf there exists an integer i satisfying the following condition, print the minimum such i; otherwise, print -1.
Sample Input 1contest
son
Sample Output 110
t = son is a subsequence of the string contestcon (the first 10 characters in s' = contestcontestcontest...), so i = 10 satisfies the condition.
On the other hand, t is not a subsequence of the string contestco (the first 9 characters in s'), so i = 9 does not satisfy the condition.
Similarly, any integer less than 9 does not satisfy the condition, either. Thus, the minimum integer i satisfying the condition is 10.
Sample Input 2contest
programming
Sample Output 2-1
t = programming is not a substring of s' = contestcontestcontest.... Thus, there is no integer i satisfying the condition.
Sample Input 3contest
sentence
Sample Output 333
Note that the answer may not fit into a 32-bit integer type, though we cannot put such a case here.

Extracted Specification

An integer N (1 ≤ N ≤ 10^5), representing the length of the first string.
A string S of length N, consisting of lowercase English letters.
An integer M (1 ≤ M ≤ 10^5), representing the length of the second string.
A string T of length M, consisting of lowercase English letters.

### Example Input:

```
7
contest
3
son
```

### Function Signature:
Write a function f(N, S, M, T) that takes in the input. 
def f(N: int, S: str, M: int, T: str): 
    ''' 
    N: an integer 
    S: a string
    M: an integer
    T: a string
    '''

Test Case Generator

Certainly! Here's a test case generator for the problem statement you provided. The generator will produce random strings `s` and `t` consisting of lowercase English letters, which can be used to test your solution:

```python
import random
import string

def tcgen():
    # Generate random lengths for s and t within the constraints
    s_length = random.randint(1, 10**5)
    t_length = random.randint(1, 10**5)
    
    # Generate random strings of the given lengths
    s = ''.join(random.choices(string.ascii_lowercase, k=s_length))
    t = ''.join(random.choices(string.ascii_lowercase, k=t_length))
    
    return s, t

# Example usage:
s, t = tcgen()
print("s:", s)
print("t:", t)
```

### Explanation:

1. **Random Lengths for `s` and `t`**:
   - `s_length`: Random integer between 1 and 100,000.
   - `t_length`: Random integer between 1 and 100,000.

2. **Random Strings Generation**:
   - `s`: Randomly chosen lowercase letters of length `s_length`.
   - `t`: Randomly chosen lowercase letters of length `t_length`.

3. **Output**:
   - The function returns two strings `s` and `t`.

You can use the generated test cases to validate the correctness and performance of your solution for the given problem statement.

Extract Arguments

def extract_arguments(fh):
    s = fh.readline().strip()
    t = fh.readline().strip()
    return s, t