CF1715D 2+ doors

The Narrator has an integer array $ a $ of length $ n $ , but he will only tell you the size $ n $ and $ q $ statements, each of them being three integers $ i, j, x $ , which means that $ a_i \mid a_j = x $ , where $ | $ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR). Find the lexicographically smallest array $ a $ that satisfies all the statements. An array $ a $ is lexicographically smaller than an array $ b $ of the same length if and only if the following holds: - in the first position where $ a $ and $ b $ differ, the array $ a $ has a smaller element than the corresponding element in $ b $ .

In the first line you are given with two integers $ n $ and $ q $ ( $ 1 \le n \le 10^5 $ , $ 0 \le q \le 2 \cdot 10^5 $ ). In the next $ q $ lines you are given with three integers $ i $ , $ j $ , and $ x $ ( $ 1 \le i, j \le n $ , $ 0 \le x < 2^{30} $ ) — the statements. It is guaranteed that all $ q $ statements hold for at least one array.

On a single line print $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i < 2^{30} $ ) — array $ a $ .

In the first sample, these are all the arrays satisfying the statements: - $ [0, 3, 2, 2] $ , - $ [2, 1, 0, 0] $ , - $ [2, 1, 0, 2] $ , - $ [2, 1, 2, 0] $ , - $ [2, 1, 2, 2] $ , - $ [2, 3, 0, 0] $ , - $ [2, 3, 0, 2] $ , - $ [2, 3, 2, 0] $ , - $ [2, 3, 2, 2] $ .