I was doing the following problem: https://csacademy.com/contest/ioi-2016-training-round-5/task/balanced-string/↵
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Basically, given a string $S$ of $A$'s and $B$'s, you want to determine whether for any two circular substrings of $S$ of the same length $l$ ( $1 \leq l \leq N, 1 ≤l≤N$ ) the number of As in the first substring and the number of As in the second substring differ by at most 1. (A circular substring is basically a substring that can wrap around S, such as $[S_n, S_1, S_2]$).↵
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The [solution](https://csacademy.com/contest/ioi-2016-training-round-5/task/balanced-string/solution/) in the editorial seems elegant, but I'm not sure how to prove its correctness.↵
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Any comments about why the solution is correct are appreciated.
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Basically, given a string $S$ of $A$'s and $B$'s, you want to determine whether for any two circular substrings of $S$ of the same length $l$ ( $1 \leq l \leq N, 1 ≤l≤N$ ) the number of As in the first substring and the number of As in the second substring differ by at most 1. (A circular substring is basically a substring that can wrap around S, such as $[S_n, S_1, S_2]$).↵
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The [solution](https://csacademy.com/contest/ioi-2016-training-round-5/task/balanced-string/solution/) in the editorial seems elegant, but I'm not sure how to prove its correctness.↵
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Any comments about why the solution is correct are appreciated.
