{"problem":{"name":"M<=ab","description":{"content":"You are given positive integers $N$ and $M$.   Find the smallest positive integer $X$ that satisfies both of the conditions below, or print $-1$ if there is no such integer. *   $X$ can be represente","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc296_d"},"statements":[{"statement_type":"Markdown","content":"You are given positive integers $N$ and $M$.  \nFind the smallest positive integer $X$ that satisfies both of the conditions below, or print $-1$ if there is no such integer.\n\n*   $X$ can be represented as the product of two integers $a$ and $b$ between $1$ and $N$, inclusive. Here, $a$ and $b$ may be the same.\n*   $X$ is at least $M$.\n\n## Constraints\n\n*   $1\\leq N\\leq 10^{12}$\n*   $1\\leq M\\leq 10^{12}$\n*   $N$ and $M$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc296_d","tags":[],"sample_group":[["5 7","8\n\nFirst, $7$ cannot be represented as the product of two integers between $1$ and $5$.  \nSecond, $8$ can be represented as the product of two integers between $1$ and $5$, such as $8=2\\times 4$.\nThus, you should print $8$."],["2 5","\\-1\n\nSince $1\\times 1=1$, $1\\times 2=2$, $2\\times 1=2$, and $2\\times 2=4$, only $1$, $2$, and $4$ can be represented as the product of two integers between $1$ and $2$, so no number greater than or equal to $5$ can be represented as the product of two such integers.  \nThus, you should print $-1$."],["100000 10000000000","10000000000\n\nFor $a=b=100000$ $(=10^5)$, the product of $a$ and $b$ is $10000000000$ $(=10^{10})$, which is the answer.  \nNote that the answer may not fit into a $32$\\-bit integer type."]],"created_at":"2026-03-03 11:01:14"}}