Problem:
Score : 300 points

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

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.

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

Solution in Python (3.4.3) (judge verdict: Runtime Error)

def main():
    import sys
    sys.setrecursionlimit(10**6)
    input = sys.stdin.readline

    def gcd(a, b):
        if b == 0:
            return a
        return gcd(b, a % b)
    
    N, M = [int(x) for x in input().strip().split()]
    S = input().strip()
    T = input().strip()
    L = (N * M) // gcd(N, M)
    ans = ['0'] * L
    for n in range(L//N):
        ans[L//N*n] = S[n%N]
    for m in range(L//M):
        if ans[(L//M)*m] == '0':
            ans[(L//M)*m] = T[m%M]
        elif ans[(L//M)*m] == T[m%M]:
            continue
        else:
            print(-1)
            return
    print(L)

if __name__ == '__main__':
    main()