B. Yet Another Convolution

Codeforces

IDCF10235B

Time6000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You are given an integer array $a_1, \\dots, a_n$ and an integer array $b_1, \\dots, b_n$. You have to calculate the array $c_1, \\dots, c_n$ defined as follows: $$c_k = \max\limits_{\gcd(i,j) = k} |a_i - b_j|\text{.}$$ The first line of input contains a single integer $n$ ($1 <= n <= 10^5$). The second line of input contains $n$ integers $a_1, \\dots, a_n$ ($1 <= a_i <= 10^9$). The third line of input contains $n$ integers $b_1, \\dots, b_n$ ($1 <= b_i <= 10^9$). Output $n$ integers $c_1, \\dots, c_n$. ## Input The first line of input contains a single integer $n$ ($1 <= n <= 10^5$).The second line of input contains $n$ integers $a_1, \\dots, a_n$ ($1 <= a_i <= 10^9$).The third line of input contains $n$ integers $b_1, \\dots, b_n$ ($1 <= b_i <= 10^9$). ## Output Output $n$ integers $c_1, \\dots, c_n$. [samples]

**Definitions** Let $ n \in \mathbb{Z}^+ $, and let $ A = (a_1, \dots, a_n) $, $ B = (b_1, \dots, b_n) $ be sequences of integers. Define $ C = (c_1, \dots, c_n) $, where for each $ k \in \{1, \dots, n\} $: **Objective** $$ c_k = \max_{\substack{1 \le i,j \le n \\ \gcd(i,j) = k}} |a_i - b_j| $$

API Response (JSON)

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