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 (1.15.1) (judge verdict: Time Limit Exceeded)

use std::collections::VecDeque;
use std::io::*;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut graph: Vec<Vec<usize>> = vec![vec![]; n];
    for _ in 0..m {
        let (a, b) = (read::<usize>() - 1, read::<usize>() - 1);
        graph[a].push(b);
        graph[b].push(a);
    }

    let mut color: Vec<i32> = vec![0; n];
    let inf = 1 << 30;
    let q: usize = read();
    for _ in 0..q {
        let (v, d, c) = (read::<usize>() - 1, read::<i32>(), read::<i32>());
        let mut que: VecDeque<usize> = VecDeque::new();
        let mut dist: Vec<i32> = vec![inf; n];
        color[v] = c;
        dist[v] = 0;
        que.push_back(v);
        while !que.is_empty() {
            let p = que.pop_front().unwrap();
            if dist[p] >= d {
                continue;
            }
            for i in &graph[p] {
                if dist[*i] == inf {
                    dist[*i] = dist[p] + 1;
                    color[*i] = c;
                    que.push_back(*i);
                }
            }
        }
    }
    for i in &color {
        println!("{}", *i);
    }
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}