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# [Solution] 2+ doors Codeforces Solution|Solution Codeforces

D. 2+ doors
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $b$.
Input

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}$).

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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.

Output

On a single line print $n$ integers ${a}_{1},{a}_{2},\dots ,{a}_{n}$ ($0\le {a}_{i}<{2}^{30}$) — array $a$.