Codeforces Round 816 (Div. 2) |
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Finished |

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2-sat

bitmasks

graphs

greedy

*1900

No tag edit access

The problem statement has recently been changed. View the changes.

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D. 2+ doors

time limit per test

1.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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:

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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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