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 $$$q$$$ ($$$1 \le n \le 10^5$$$, $$$0 \le q \le 2 \cdot 10^5$$$).

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 $$$a$$$.

Examples
Input
4 3
1 2 3
1 3 2
4 1 2
Output
0 3 2 2
Input
1 0
Output
0
Input
2 1
1 1 1073741823
Output
1073741823 0
Note

In the first sample, these are all the arrays satisfying the statements:

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