Problem:
Score : 700 points

Problem Statement

Squid loves painting vertices in graphs.

There is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.
Initially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.

Squid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.

Find the color of each vertex after the Q operations.

Constraints

1 ≤ N,M,Q ≤ 10^5

1 ≤ a_i,b_i,v_i ≤ N

a_i ≠ b_i

0 ≤ d_i ≤ 10

1 ≤ c_i ≤10^5

d_i and c_i are all integers.

There are no self-loops or multiple edges in the given graph.

Partial Score

200 points will be awarded for passing the testset satisfying 1 ≤ N,M,Q ≤ 2{,}000.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_{M} b_{M}
Q
v_1 d_1 c_1
:
v_{Q} d_{Q} c_{Q}

Output

Print the answer in N lines.
In the i-th line, print the color of vertex i after the Q operations.

Sample Input 1

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2

Sample Output 1

2
2
2
2
2
1
0

Initially, each vertex is painted in color 0.
In the first operation, vertices 5 and 6 are repainted in color 1.
In the second operation, vertices 1, 2, 3, 4 and 5 are repainted in color 2.

Sample Input 2

14 10
1 4
5 7
7 11
4 10
14 7
14 3
6 14
8 11
5 13
8 3
8
8 6 2
9 7 85
6 9 3
6 7 5
10 3 1
12 9 4
9 6 6
8 2 3

Sample Output 2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.

Solution in Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

use proconio::{input, fastout};

// ABC086C - Traveling
// https://atcoder.jp/contests/abs/fasks/arc089_a

#[fastout]
fn main() {
    input! {
        n :usize,
        m :usize,
        ab :[(usize, usize); m],
        q :usize,
        vdc :[(usize, usize, usize); q]
    }

    let mut neighbors = vec![Vec::new();n];
    for (a, b) in ab {
        neighbors[a-1].push(b);
        neighbors[b-1].push(a);
    }
    
    let mut color = vec![0;n];
    let mut painted_radius = vec![-1;n];
    for &(v, d, c) in vdc.iter().rev() {
        paint(v, d, c, &neighbors, &mut color, &mut painted_radius);
    }

    for c in color {
        println!("{}", c);
    }
}

fn paint(v :usize, d :usize, c :usize, neighbors :&Vec<Vec<usize>>, color :&mut Vec<usize>, painted_radius :&mut Vec<isize>) {
    if painted_radius[v-1] >= d as isize {
        return;
    }
    if color[v-1] == 0 {
        color[v-1] = c;
    }
    painted_radius[v-1] = d as isize;
    if d > 0 {
        for &w in &neighbors[v-1] {
            paint(w, d-1, c, neighbors, color, painted_radius);
        }
    }
}