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: Accepted)

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 q: usize = read();
    let vdc: Vec<(usize, usize, i32)> = (0..q)
        .map(|_| (read::<usize>() - 1, read::<usize>(), read::<i32>()))
        .collect();

    let mut dp: Vec<Vec<usize>> = vec![vec![q; 11]; n];
    for i0 in 0..q {
        let i = q - i0 - 1;
        let (v, d, _) = vdc[i];
        let mut que: VecDeque<(usize, usize)> = VecDeque::new();
        if dp[v][d] == q {
            dp[v][d] = i;
        }
        if graph[v].is_empty() {
            for j in 0..d {
                if dp[v][j] == q {
                    dp[v][j] = i;
                }
            }
            continue;
        }
        que.push_back((v, d));
        while !que.is_empty() {
            let (p, dist) = que.pop_front().unwrap();
            if dist <= 0 {
                continue;
            }
            if dp[p][dist - 1] == q {
                dp[p][dist - 1] = i;
            }
            for j in &graph[p] {
                if dp[*j][dist - 1] == q {
                    dp[*j][dist - 1] = i;
                    que.push_back((*j, dist - 1));
                }
            }
        }
    }
    for i in 0..n {
        if dp[i][0] == q {
            println!("{}", 0);
        } else {
            println!("{}", vdc[dp[i][0]].2);
        }
    }
}

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")
}