2+ doors

## 题目描述 Narrator有一个长度为 $n$ 的整数数组 $a$ ，但是他只会告诉你 $n$ 的大小和 $q$ 个要求，每个要求包括三个整数 $i,j,x$ ，要求满足 $a_i\mid a_j = x$，其中 $|$ 表示按位或运算 找到满足所有要求的字典序最小的数组 $a$ ## 输入格式 第一行读入两个整数 $n$ 和 $q$ ( $1 \le n \le 10^5$ , $0 \le q \le 2 \cdot 10^5$ ) 接下来 $q$ 行，读入三个整数 $i$ , $j$ , $x$ ( $1 \le i, j \le n $ , $ 0 \le x < 2^{30} $ ) 保证所有 $q$ 个要求至少满足一个数组 $a$ ## 输出格式 一行 $n$ 个整数 $a_1, a_2, \ldots, a_n$ ( $0 \le a_i < 2^{30}$ )

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 $ .

4 3
1 2 3
1 3 2
4 1 2

0 3 2 2

1 0

0

2 1
1 1 1073741823

1073741823 0

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] $ .