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::io::{BufRead, Write};
use std::io;

fn paint(colors: &mut Vec<(u32, i32)>,
         index: usize,
         color: u32,
         distance: i32,
         adjacency: &Vec<Vec<u32>>) {
    if distance > colors[index].1 {
        if colors[index].1 == -1 {
            colors[index] = (color, distance);
        }
        for item in &adjacency[index] {
            paint(colors, *item as usize, color, distance - 1, adjacency);
        }
    }
}

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let mut split = s.split_whitespace();
    let n = split.next().unwrap().parse::<u32>().unwrap();
    let m = split.next().unwrap().parse::<u32>().unwrap();
    let mut s = String::new();
    let mut colors = vec![(0u32,-1i32);n as usize];
    let mut adjacency = vec![Vec::<u32>::with_capacity(8);n as usize];
    for _ in 0..m {
        s.clear();
        input.read_line(&mut s).unwrap();
        let mut split = s.split_whitespace();
        let a = split.next().unwrap().parse::<u32>().unwrap();
        let b = split.next().unwrap().parse::<u32>().unwrap();
        adjacency[a as usize - 1].push(b - 1);
        adjacency[b as usize - 1].push(a - 1);
    }
    s.clear();
    input.read_line(&mut s).unwrap();
    let q = s.trim().parse::<usize>().unwrap();
    let vdc = (0..q)
        .map(|_| {
            s.clear();
            input.read_line(&mut s).unwrap();
            let mut split = s.split_whitespace();
            let v = split.next().unwrap().parse::<u32>().unwrap();
            let d = split.next().unwrap().parse::<i32>().unwrap();
            let c = split.next().unwrap().parse::<u32>().unwrap();
            (v, d, c)
        })
        .collect::<Vec<_>>();
    for (v, d, c) in vdc.into_iter().rev() {
        paint(&mut colors, v as usize - 1, c, d, &adjacency);
    }
    for (c, _) in colors {
        writeln!(output, "{}", c).unwrap();
    }
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2\n",
             "2
2
2
2
2
1
0\n");
    }
    #[test]
    fn case2() {
        test("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\n",
             "1
0
3
1
5
5
3
3
6
1
3
4
5
3\n");
    }
}