{"raw_statement":[{"iden":"problem statement","content":"You are given a string $S$ of length $N$ and another string $T$ of length $M$. These strings consist of lowercase English letters.\nA string $X$ is called a **good string** when the following conditions are all met:\n\n*   Let $L$ be the length of $X$. $L$ is divisible by both $N$ and $M$.\n*   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 $S$.\n*   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 $T$.\n\nDetermine if there exists a good string. If it exists, find the length of the shortest such string."},{"iden":"constraints","content":"*   $1 \\leq N,M \\leq 10^5$\n*   $S$ and $T$ consist of lowercase English letters.\n*   $|S|=N$\n*   $|T|=M$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$S$\n$T$"},{"iden":"sample input 1","content":"3 2\nacp\nae"},{"iden":"sample output 1","content":"6\n\nFor example, the string `accept` is a good string. There is no good string shorter than this, so the answer is $6$."},{"iden":"sample input 2","content":"6 3\nabcdef\nabc"},{"iden":"sample output 2","content":"\\-1"},{"iden":"sample input 3","content":"15 9\ndnsusrayukuaiia\ndujrunuma"},{"iden":"sample output 3","content":"45"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}