{"problem":{"name":"Strings of Eternity","description":{"content":"Given are two strings $s$ and $t$ consisting of lowercase English letters. Determine if the number of non-negative integers $i$ satisfying the following condition is finite, and find the maximum value","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc135_f"},"statements":[{"statement_type":"Markdown","content":"Given are two strings $s$ and $t$ consisting of lowercase English letters. Determine if the number of non-negative integers $i$ satisfying the following condition is finite, and find the maximum value of such $i$ if the number is finite.\n\n*   There exists a non-negative integer $j$ such that the concatenation of $i$ copies of $t$ is a substring of the concatenation of $j$ copies of $s$.\n\n## Constraints\n\n*   $1 \\leq |s| \\leq 5 \\times 10^5$\n*   $1 \\leq |t| \\leq 5 \\times 10^5$\n*   $s$ and $t$ consist of lowercase English letters.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$s$\n$t$\n\n[samples]\n\n## Notes\n\n*   A string $a$ is a substring of another string $b$ if and only if there exists an integer $x$ $(0 \\leq x \\leq |b| - |a|)$ such that, for any $y$ $(1 \\leq y \\leq |a|)$, $a_y = b_{x+y}$ holds.\n    \n*   We assume that the concatenation of zero copies of any string is the empty string. From the definition above, the empty string is a substring of any string. Thus, for any two strings $s$ and $t$, $i = 0$ satisfies the condition in the problem statement.","is_translate":false,"language":"English"}],"meta":{"iden":"abc135_f","tags":[],"sample_group":[["abcabab\nab","3\n\nThe concatenation of three copies of $t$, `ababab`, is a substring of the concatenation of two copies of $s$, `abcabababcabab`, so $i = 3$ satisfies the condition.\nOn the other hand, the concatenation of four copies of $t$, `abababab`, is not a substring of the concatenation of any number of copies of $s$, so $i = 4$ does not satisfy the condition.\nSimilarly, any integer greater than $4$ does not satisfy the condition, either. Thus, the number of non-negative integers $i$ satisfying the condition is finite, and the maximum value of such $i$ is $3$."],["aa\naaaaaaa","\\-1\n\nFor any non-negative integer $i$, the concatenation of $i$ copies of $t$ is a substring of the concatenation of $4i$ copies of $s$. Thus, there are infinitely many non-negative integers $i$ that satisfy the condition."],["aba\nbaaab","0\n\nAs stated in Notes, $i = 0$ always satisfies the condition."]],"created_at":"2026-03-03 11:01:14"}}