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G - Prefix Concatenation

Score : $600$ points

Problem Statement

You are given two strings $S$ and $T$ consisting of lowercase English letters.

Find the minimum positive integer $k$ such that you can choose (not necessarily distinct) $k$ prefixes of $S$ so that their concatenation coincides with $T$.

In other words, find the minimum positive integer $k$ such that there exists a $k$-tuple $(a_1,a_2,\ldots, a_k)$ of integers between $1$ and $|S|$ such that
$T=S_{a_1}+S_{a_2}+\cdots +S_{a_k}$, where $S_i$ denotes the substring of $S$ from the $1$-st through the $i$-th characters and $+$ denotes the concatenation of strings.

If it is impossible to make it coincide with $T$, print $-1$ instead.

Constraints

• $1 \leq |S| \leq 5\times 10^5$
• $1 \leq |T| \leq 5\times 10^5$
• $S$ and $T$ are strings consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$S$

$T$

Output

Print the minimum positive integer $k$ such that you can choose $k$ prefixes of $S$ so that their concatenation coincides with $T$. It is impossible to make it coincide with $T$, print $-1$ instead.

aba
ababaab

3

$T=$ ababaab can be written as ab + aba + ab, of which ab and aba are prefixes of $S=$ aba.
Since it is unable to express ababaab with two or less prefixes of aba, print $3$.

atcoder
ac

-1

Since it is impossible to express $T$ as a concatenation of prefixes of $S$, print $-1$.