{"problem":{"name":"Number of Digits","description":{"content":"For a positive integer $n$, let us define $f(n)$ as the number of digits in base $10$. You are given an integer $S$. Count the number of the pairs of positive integers $(l, r)$ ($l \\leq r$) such that ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc090_d"},"statements":[{"statement_type":"Markdown","content":"For a positive integer $n$, let us define $f(n)$ as the number of digits in base $10$.\nYou are given an integer $S$. Count the number of the pairs of positive integers $(l, r)$ ($l \\leq r$) such that $f(l) + f(l + 1) + ... + f(r) = S$, and find the count modulo $10^9 + 7$.\n\n## Constraints\n\n*   $1 \\leq S \\leq 10^8$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$S$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc090_d","tags":[],"sample_group":[["1","9\n\nThere are nine pairs $(l, r)$ that satisfies the condition: $(1, 1)$, $(2, 2)$, $...$, $(9, 9)$."],["2","98\n\nThere are $98$ pairs $(l, r)$ that satisfies the condition, such as $(1, 2)$ and $(33, 33)$."],["123","460191684"],["36018","966522825"],["1000","184984484"]],"created_at":"2026-03-03 11:01:14"}}