{"problem":{"name":"Digit Sums","description":{"content":"Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(101) = 1 + 0 + 1 = 2$. Given an integer $N$, determine if $S(N)$ divides $N$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc101_b"},"statements":[{"statement_type":"Markdown","content":"Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(101) = 1 + 0 + 1 = 2$.\nGiven an integer $N$, determine if $S(N)$ divides $N$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"设 $S(n)$ 表示 $n$ 的十进制表示中各位数字之和。例如，$S(101) = 1 + 0 + 1 = 2$。\n给定一个整数 $N$，判断 $S(N)$ 是否能整除 $N$。\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^9$\n\n## Input\n\n输入从标准输入给出，格式如下：\n\n$N$\n\n[samples]","is_translate":true,"language":"Chinese"},{"statement_type":"Markdown","content":"### Definitions\n- For $n\\in\\mathbb{Z}_{\\ge 0}$ with decimal expansion $n=\\sum_{i=0}^{k} d_i 10^i$, where $k\\in\\mathbb{Z}_{\\ge 0}$ and $d_i\\in\\{0,1,\\dots,9\\}$, define\n$$\nS(n)=\\sum_{i=0}^{k} d_i .\n$$\n\n### Given\n- $N\\in\\mathbb{Z}_{\\ge 0}$.\n\n### Objective\n- Determine whether $S(N)\\mid N$, i.e.\n$$\n\\exists q\\in\\mathbb{Z}\\ \\text{such that}\\ N=q\\,S(N).\n$$","is_translate":false,"language":"Formal"}],"meta":{"iden":"abc101_b","tags":[],"sample_group":[["12","Yes\n\nIn this input, $N=12$. As $S(12) = 1 + 2 = 3$, $S(N)$ divides $N$."],["101","No\n\nAs $S(101) = 1 + 0 + 1 = 2$, $S(N)$ does not divide $N$."],["999999999","Yes"]],"created_at":"2026-03-03 11:01:13"}}