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;
use std::io::Read;
use std::collections::VecDeque;

fn main() {
    let mut stdin = io::stdin();
    let mut lines = String::new();
    let _ = stdin.read_to_string(&mut lines);
    let vec = lines.lines().collect::<Vec<&str>>();
    let vec0 = vec[0].split(' ').collect::<Vec<&str>>();
    let n :usize = vec0[0].trim().parse().unwrap();
    let m :usize = vec0[1].trim().parse().unwrap();
    let mut ab :Vec<(usize,usize)> = Vec::new();
    for i in 0..m {
        let veci1 = vec[i+1].split(' ').collect::<Vec<&str>>();
        let a :usize = veci1[0].trim().parse().unwrap();
        let b :usize = veci1[1].trim().parse().unwrap();
        ab.push((a,b));
    }
    let ab = ab;
    let q :usize = vec[m+1].trim().parse().unwrap();
    let mut vdc :Vec<(usize,usize,usize)> = Vec::new();
    for j in 0..q {
        let vecjm2 = vec[j+m+2].split(' ').collect::<Vec<&str>>();
        let v :usize = vecjm2[0].trim().parse().unwrap();
        let d :usize = vecjm2[1].trim().parse().unwrap();
        let c :usize = vecjm2[2].trim().parse().unwrap();
        vdc.push((v,d,c));
    }

    let mut nutta :Vec<usize> = vec![0;n];
    let mut color :Vec<usize> = vec![0;n];
    for j in 0..q {
        let mut queue :VecDeque<(usize,usize,usize)> = VecDeque::new();
        queue.push_back(vdc[q-1-j]);
        while let Some((v,d,c)) = queue.pop_front() {
            if nutta[v-1] > d { continue; }
            nutta[v-1] = d+1;
            if color[v-1] == 0 {
                color[v-1] = c;
            }
            if d > 0 {
                for k in 0..m {
                    let (a,b) = ab[k];
                    if a == v {
                        queue.push_back((b,d-1,c));
                    } else if b == v {
                        queue.push_back((a,d-1,c));
                    }
                }
            }
        }
    }
    for i in 0..n {
        println!("{}",color[i]);
    }
}