2+ doors
Description
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 $a$.
Input
In the first line you are given with two integers $n$ and $q$ ($1 \le n \le 10^5$, $0 \le q \le 2 \cdot 10^5$).
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 $a_1, a_2, \ldots, a_n$ ($0 \le a_i < 2^{30}$) — array $a$.
Samples
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
Note
In the first sample, these are all the arrays satisfying the statements:
- $[0, 3, 2, 2]$,
- $[2, 1, 0, 0]$,
- $[2, 1, 0, 2]$,
- $[2, 1, 2, 0]$,
- $[2, 1, 2, 2]$,
- $[2, 3, 0, 0]$,
- $[2, 3, 0, 2]$,
- $[2, 3, 2, 0]$,
- $[2, 3, 2, 2]$.