AT_abc444_c [ABC444C] AtCoder Riko

You are given a sequence of $ N $ positive integers $ A=(A_1,A_2,\dots,A_N) $ . Find all positive integers $ L $ for which the following can occur: > AtCoder Inc. has released a stick-shaped snack called "AtCoderiko." A cup contains one or more AtCoderikos, each of length $ L $ . When Takahashi shook the cup, each AtCoderiko ended up in one of the following states: > > - It remained as one AtCoderiko of length $ L $ . > - It broke into two AtCoderikos whose lengths sum to $ L $ . Here, the length of each AtCoderiko is a positive integer. > > After shaking the cup, there were $ N $ AtCoderikos in the cup, and the length of the $ i $ -th AtCoderiko was $ A_i $ . The given input guarantees that there exists at least one positive integer $ L $ for which this can occur.

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output all values of $ L $ satisfying the condition in ascending order, separated by spaces, in one line.

### Sample Explanation 1 If the cup initially contained three AtCoderikos of length $ 10 $ , and one of them broke into two AtCoderikos of length $ 5 $ , the condition is satisfied. If the cup initially contained two AtCoderikos of length $ 15 $ , and each of them broke into two AtCoderikos of lengths $ 5 $ and $ 10 $ , the condition is satisfied. No other values of $ L $ satisfy the condition. ### Constraints - $ 1 \leq N \leq 3 \times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - There exists at least one $ L $ satisfying the condition. - All input values are integers.