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.

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:

• $[0, 3, 2, 2]$ ,
• $[2, 1, 0, 0]$ ,
• $[2, 1, 0, 2]$ ,
• $[2, 1, 2, 0]$ ,
• $[2, 1, 2, 2]$ ,
• $[2, 3, 0, 0]$ ,
• $[2, 3, 0, 2]$ ,
• $[2, 3, 2, 0]$ ,
• $[2, 3, 2, 2]$ .