{"raw_statement":[{"iden":"problem statement","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 $b$."},{"iden":"constraints","content":"*   $1 \\leq n \\leq 10^{11}$\n*   $1 \\leq s \\leq 10^{11}$\n*   $n,\\,s$ are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$n$\n$s$"},{"iden":"sample input 1","content":"87654\n30"},{"iden":"sample output 1","content":"10"},{"iden":"sample input 2","content":"87654\n138"},{"iden":"sample output 2","content":"100"},{"iden":"sample input 3","content":"87654\n45678"},{"iden":"sample output 3","content":"\\-1"},{"iden":"sample input 4","content":"31415926535\n1"},{"iden":"sample output 4","content":"31415926535"},{"iden":"sample input 5","content":"1\n31415926535"},{"iden":"sample output 5","content":"\\-1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}