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)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let (N, M): (usize, usize) = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap()
        )
    };
    let (a, b): (Vec<usize>, Vec<usize>) = {
        let (mut a, mut b) = (vec![], vec![]);
        for _ in 0..M {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            a.push(iter.next().unwrap().parse().unwrap());
            b.push(iter.next().unwrap().parse().unwrap());
        }
        (a, b)
    };
    let Q: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let (v, d, c): (Vec<usize>, Vec<usize>, Vec<usize>) = {
        let (mut v, mut d, mut c) = (vec![], vec![], vec![]);
        for _ in 0..Q {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            v.push(iter.next().unwrap().parse().unwrap());
            d.push(iter.next().unwrap().parse().unwrap());
            c.push(iter.next().unwrap().parse().unwrap());
        }
        (v, d, c)
    };

    // 最後の操作から順に処理
    // 拡張グラフに対してDFSすることで計算量を抑える
    let G = {
        let mut G = vec![std::collections::HashSet::new(); N + 1];
        for i in 0..M {
            G[a[i]].insert(b[i]);
            G[b[i]].insert(a[i]);
        }
        G
    };
    fn f(x: usize, dist: usize, color: usize,
        G: &Vec<std::collections::HashSet<usize>>, res: &mut Vec<usize>, reacheable: &mut Vec<Vec<bool>>) {
        if reacheable[x][dist] {
            reacheable[x][dist] = false;
            if res[x] == 0 { res[x] = color; }
            if dist > 0 {
                for &y in &G[x] { f(y, dist - 1, color, &G, res, reacheable); }
            }
        }
    }
    let mut res = vec![0; N + 1];
    let mut reacheable = vec![vec![true; 11]; N + 1];
    for i in (0..Q).rev() { f(v[i], d[i], c[i], &G, &mut res, &mut reacheable); }
    let ans = res[1..].iter()
        .map(std::string::ToString::to_string)
        .collect::<Vec<_>>()
        .join("\n");

    println!("{}", ans);
}