Problem Statement

A kingdom has $N$ towns, numbered from $1$ to $N$. In town $i$ ( $i = 1, 2, \ldots, N$ ) there are $X_i$ houses, and for now all that is known is that $0 \leq X_i < 2^{30}$. The king of this country wants to know how many houses each town has.

One day, $M$ travelers visited this country. The $j$-th traveler ( $j = 1, 2, \ldots, M$ ) toured 2 of the towns in the kingdom: town $A_j$ and town $B_j$. When leaving the kingdom, each traveler $j$ reported the following 2 things to the king.

• The numbers $A_j$ , $B_j$ of the towns they toured.
• The value $Y_j$ obtained by taking the XOR of the numbers of houses in the 2 towns they toured. That is, $$Y_j = X_{A_j} \oplus X_{B_j}$$

The king decided to determine the number of houses in each town, $X_1, X_2, \ldots, X_N$, based on the reports of the $M$ travelers.

However, some of the travelers may have made false reports.

If there exists a set of values $X_1, X_2, \ldots, X_N$ consistent with all of the reports of the $M$ travelers, output one of them. Otherwise (when the travelers' reports are contradictory), output $-1$.

Input

$N$ $M$
$A_1$ $B_1$
$Y_1$
$A_2$ $B_2$
$Y_2$
$\vdots$
$A_M$ $B_M$
$Y_M$

Constraints:

• All inputs are integers.
• $1 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• For each $j = 1, 2, \ldots, M$:
  • $1 \leq A_j < B_j \leq N$
  • $0 \leq Y_i < 2^{30}$

Output

If there is no contradiction, output, separated by newlines,

$X_1$
$X_2$
$\vdots$
$X_N$

If there is a contradiction, output

-1

Sample

3 3
1 2
3
2 3
5
1 3
6

2
1
4

2 2
1 2
1
1 2
2

-1