RU-ALLRUSSIAN 2021 Problem 117

Find all permutations $(a_1, a_2,...,a_{2021})$ of $(1,2,...,2021)$ , such that for every two positive integers $m$ and $n$ with difference bigger than $20^{21}$ , the following inequality holds: $GCD(m+1, n+a_1)+GCD(m+2, n+a_2)+...+GCD(m+2021, n+a_{2021})<2|m-n|$ .