{"problem":{"name":"Digit Sum","description":{"content":"For integers $b (b \\geq 2)$ and $n (n \\geq 1)$, let the function $f(b,n)$ be defined as follows: *   $f(b,n) = n$, when $n < b$ *   $f(b,n) = f(b,\\,{\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b)$, when $n","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc060_b"},"statements":[{"statement_type":"Markdown","content":"For integers $b (b \\geq 2)$ and $n (n \\geq 1)$, let the function $f(b,n)$ be defined as follows:\n\n*   $f(b,n) = n$, when $n < b$\n*   $f(b,n) = f(b,\\,{\\rm floor}(n / b)) + (n \\ {\\rm mod} \\ b)$, when $n \\geq b$\n\nHere, ${\\rm floor}(n / b)$ denotes the largest integer not exceeding $n / b$, and $n \\ {\\rm mod} \\ b$ denotes the remainder of $n$ divided by $b$.\nLess formally, $f(b,n)$ is equal to the sum of the digits of $n$ written in base $b$. For example, the following hold:\n\n*   $f(10,\\,87654)=8+7+6+5+4=30$\n*   $f(100,\\,87654)=8+76+54=138$\n\nYou are given integers $n$ and $s$. Determine if there exists an integer $b (b \\geq 2)$ such that $f(b,n)=s$. If the answer is positive, also find the smallest such $b$.\n\n## Constraints\n\n*   $1 \\leq n \\leq 10^{11}$\n*   $1 \\leq s \\leq 10^{11}$\n*   $n,\\,s$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$n$\n$s$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc060_b","tags":[],"sample_group":[["87654\n30","10"],["87654\n138","100"],["87654\n45678","\\-1"],["31415926535\n1","31415926535"],["1\n31415926535","\\-1"]],"created_at":"2026-03-03 11:01:13"}}