Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Best Edge Weight

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a connected weighted graph with *n* vertices and *m* edges. The graph doesn't contain loops nor multiple edges. Consider some edge with id *i*. Let's determine for this edge the maximum integer weight we can give to it so that it is contained in all minimum spanning trees of the graph if we don't change the other weights.

You are to determine this maximum weight described above for each edge. You should calculate the answer for each edge independently, it means there can't be two edges with changed weights at the same time.

Input

The first line contains two integers *n* and *m* (2 ≤ *n* ≤ 2·10^{5}, *n* - 1 ≤ *m* ≤ 2·10^{5}), where *n* and *m* are the number of vertices and the number of edges in the graph, respectively.

Each of the next *m* lines contains three integers *u*, *v* and *c* (1 ≤ *v*, *u* ≤ *n*, *v* ≠ *u*, 1 ≤ *c* ≤ 10^{9}) meaning that there is an edge between vertices *u* and *v* with weight *c*.

Output

Print the answer for each edge in the order the edges are given in the input. If an edge is contained in every minimum spanning tree with any weight, print -1 as the answer.

Examples

Input

4 4

1 2 2

2 3 2

3 4 2

4 1 3

Output

2 2 2 1

Input

4 3

1 2 2

2 3 2

3 4 2

Output

-1 -1 -1

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/19/2018 11:16:44 (d1).

Desktop version, switch to mobile version.

User lists

Name |
---|