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.

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