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Problem Statement

Given 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.

Sample Input 1

abcabab
ab

Sample Output 1

3

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 2

aa
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 3

aba
baaab

Sample Output 3

0

As stated in Notes, $i = 0$ always satisfies the condition.