CF1028E Restore Array

While discussing a proper problem A for a Codeforces Round, Kostya created a cyclic array of positive integers $ a_1, a_2, \ldots, a_n $ . Since the talk was long and not promising, Kostya created a new cyclic array $ b_1, b_2, \ldots, b_{n} $ so that $ b_i = (a_i \mod a_{i + 1}) $ , where we take $ a_{n+1} = a_1 $ . Here $ mod $ is the [modulo operation](https://en.wikipedia.org/wiki/Modulo_operation). When the talk became interesting, Kostya completely forgot how array $ a $ had looked like. Suddenly, he thought that restoring array $ a $ from array $ b $ would be an interesting problem (unfortunately, not A).

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In the first example: - $ 1 \mod 3 = 1 $ - $ 3 \mod 5 = 3 $ - $ 5 \mod 2 = 1 $ - $ 2 \mod 1 = 0 $