Problem Statement

You are given a string S of length N and another string T of length M.
These strings consist of lowercase English letters.
A string X is called a good string when the following conditions are all met:

• Let L be the length of X. L is divisible by both N and M.
• Concatenating the $1-st, (\frac{L}{N}+1)-th, (2 \times \frac{L}{N}+1)-th, ..., ((N-1)\times\frac{L}{N}+1)-th$ characters of X, without changing the order, results in S.
• Concatenating the $1-st, (\frac{L}{M}+1)-th, (2 \times \frac{L}{M}+1)-th, ..., ((M-1)\times\frac{L}{M}+1)-th$ characters of X, without changing the order, results in T.

Determine if there exists a good string. If it exists, find the length of the shortest such string.

Input

Input is given from Standard Input in the following format:
N M
S
T

Output

If a good string does not exist, print -1; if it exists, print the length of the shortest such string.

Constraints

• $1 \leq N,M \leq 10^5$
• S and T consist of lowercase English letters.
• |S|=N
• |T|=M

Sample Input 1

3 2
acp
ae

Sample Output 1

6

For example, the string accept is a good string.
There is no good string shorter than this, so the answer is 6.

Sample Input 2

6 3
abcdef
abc

Sample Output 2

-1

Sample Input 3

15 9
dnsusrayukuaiia
dujrunuma

Sample Output 3

45

见题面 Input 部分

见题面 Output 部分