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)

fn main() {
  let (n, m) = get::tuple::<usize,usize>();
  let es = get::tuples::<usize,usize>(m).iter().map(|&(a,b)|(a-1,b-1)).collect::<Vec<_>>();
  let q = get::val::<usize>();
  let qs = get::tuple3s::<usize,usize,usize>(q).iter().map(|&(v,d,c)|(v-1,d,c)).collect::<Vec<_>>();

  let g = Graph::new_nonlabeled(n, &es);
  let mut cs = vec![0; n];

  for &(v,d,c) in &qs {
    let ws = g.step(v,d);
    for w in ws {cs[w] = c}
  }

  put::vec(&cs, "\n")
}

struct Graph {
  size: usize,
  adj: Vec<Vec<(usize, isize)>>
}

impl Clone for Graph {
  fn clone(&self) -> Graph {
    Graph {
      size: self.size,
      adj: self.adj.clone()
    }
  }
}

#[allow(dead_code)]
impl Graph {
  fn new_nonlabeled(n: usize, edges: &[(usize, usize)]) -> Graph {
    let edges = edges.iter().map(|&(a,b)|(a,b,0isize)).collect::<Vec<_>>();
    Graph::new_labeled(n, &edges)
  }

  fn new_labeled(n: usize, edges: &[(usize, usize, isize)]) -> Graph {
    let mut g: Vec<Vec<(usize, isize)>> = vec![vec![]; n];
    for &(a, b, c) in edges {
      g[a].push((b,c));
      g[b].push((a,c));  // delete for digraph
    }
    Graph {size: n, adj: g}
  }

  fn is_connected(&self) -> bool {
    self.dfs(0).len() == self.size
  }

  fn is_hitofude(&self) -> bool {
    let ploop = self.adj.iter().all(|vs|vs.len()%2==0);
    let pnloop = self.adj.iter().filter(|vs|vs.len()%2==1).count() == 2;
    ploop || pnloop
  }

  fn size(&self) -> usize {
    self.size
  }

  fn edges(&self) -> Vec<(usize, usize, isize)> {
    let mut buf = vec![];
    for (i, next) in self.adj.iter().enumerate() {
      for &(j, x) in next {
        buf.push((i, j, x))
      }
    }
    buf
  }

  fn bellman_ford(&self, s: usize) -> Vec<isize> {
    const INF: isize = std::isize::MAX >> 1;
    let edges = self.edges();
    let mut bf: Vec<isize> = vec![INF; self.size];
    bf[s] = 0;

    for _ in 1 .. self.size {
      for &(v, w, c) in &edges {
        bf[w] = std::cmp::min(bf[w], bf[v]+c)
      }
    }
    bf
  }

  fn dijkstra(&self, s: usize) -> Vec<isize> {
    use std::collections::BinaryHeap;

    const INF: isize = std::isize::MAX;
    let mut dk: Vec<isize> = vec![INF; self.size];
    dk[s] = 0;

    let mut pq = BinaryHeap::new();
    pq.push((0,s));

    while let Some((acc,v)) = pq.pop() {
      let acc = -acc;
      for &(w,c) in &self.adj[v] {
        let cand = acc + c;
        if cand < dk[w] {
          dk[w] = cand;
          pq.push((-cand,w));
        }
      }
    }
    dk
  }

  fn warshall_floyd(&self) -> Vec<Vec<isize>> {
    const INF: isize = std::isize::MAX >> 1;
    let mut wf: Vec<Vec<isize>> = vec![vec![INF; self.size]; self.size];
    for i in 0 .. self.size {wf[i][i] = 0}

    for (i, next) in self.adj.iter().enumerate() {
      for &(j, x) in next {
        wf[i][j] = x
      }
    }
    for k in 0 .. self.size {
      for i in 0 .. self.size {
        for j in 0 .. self.size {
          wf[i][j] = std::cmp::min(wf[i][j], wf[i][k] + wf[k][j]);
        }
      }
    }
    wf
  }

  fn coloring2(&self) -> Option<(Vec<usize>, Vec<usize>)> {
    fn paint(v: usize, p: bool, g: &Graph, cv: &mut Vec<Option<bool>>) -> bool {
      match cv[v] {
        None => {
          let next = &g.adj[v];
          cv[v] = Some(p);
          next.iter().all(|&(w,_)|paint(w,!p,g,cv))},
        Some(q) => {q == p}
      }
    }

    let mut canvas: Vec<Option<bool>> = vec![None; self.size];
    let ans = paint(0, false, self, &mut canvas);
    let bs = canvas.iter().enumerate().filter(|&(_,&v)|v==Some(false)).map(|(i,_)|i).collect::<Vec<_>>();
    let ws = canvas.iter().enumerate().filter(|&(_,&v)|v==Some(true)).map(|(i,_)|i).collect::<Vec<_>>();
    if ans {Some((bs,ws))} else {None}
  }

  fn dfs(&self, s: usize) -> Vec<usize> {
    fn go(g: &Graph, current: usize, mut path: &mut Vec<usize>, mut visited: &mut Vec<bool>) {
      for &(next, _) in &g.adj[current] {
        if visited[next] {
          continue
        } else {
          visited[next] = true;
          path.push(next);
          go(&g, next, &mut path, &mut visited)
        }
      }
    }

    let mut path = vec![s];
    let mut visited = vec![false; self.adj.len()];
    visited[s] = true;
    go(&self, s, &mut path, &mut visited);
    path
  }

  fn step(&self, v: usize, d: usize) -> Vec<usize> {
    fn go(g: &Graph, w: usize, k: usize, ws: &mut Vec<usize>) {
      ws.push(w);
      if k == 0 {
        return
      } else {
        for &(next, _) in &g.adj[w] {
          go(g, next, k-1, ws)
        }
      }
    }
    
    let mut ws = vec![];
    go(&self, v, d, &mut ws);
    ws
  }

  fn cut(&mut self, v: usize, w: usize) {
    self.adj[v].retain(|&(t,_)| t != w);
    self.adj[w].retain(|&(t,_)| t != v);
  }
}

#[allow(dead_code)]
mod modulo {
  pub const MOD: u64 = 1_000_000_007;

  pub fn plus(x: u64, y: u64) -> u64 {
    (x + y) % MOD
  }

  pub fn mul(x: u64, y: u64) -> u64 {
    (x * y) % MOD
  }

  pub fn pow(x: u64, n: u64) -> u64 {
    match n {
      0 => 1,
      _ if n % 2 == 1 => mul(x, pow(x, n-1)),
      _ => {
        let q = pow(x, n>>1);
        mul(q, q)
      }
    }
  }
}


#[allow(dead_code)]
mod get {
  use std::io::*;
  use std::str::*;

  pub fn val<T: FromStr>() -> T {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    buf.trim_right().parse::<T>().ok().unwrap()
  }

  pub fn vals<T: FromStr>(n: usize) -> Vec<T> {
    let mut vec: Vec<T> = vec![];
    for _ in 0 .. n {
      vec.push(val());
    }
    vec
  }

  pub fn tuple<T1: FromStr, T2: FromStr>() -> (T1, T2) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    (x, y)
  }

  pub fn tuples<T1: FromStr, T2: FromStr>(n: usize) -> Vec<(T1, T2)> {
    let mut vec: Vec<(T1, T2)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple());
    }
    vec
  }

  pub fn tuple3<T1: FromStr, T2: FromStr, T3: FromStr>() -> (T1, T2, T3) {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    let mut it = buf.trim_right().split_whitespace();
    let x = it.next().unwrap().parse::<T1>().ok().unwrap();
    let y = it.next().unwrap().parse::<T2>().ok().unwrap();
    let z = it.next().unwrap().parse::<T3>().ok().unwrap();
    (x, y, z)
  }

  pub fn tuple3s<T1: FromStr, T2: FromStr, T3: FromStr>(n: usize) -> Vec<(T1, T2, T3)> {
    let mut vec: Vec<(T1, T2, T3)> = vec![];
    for _ in 0 .. n {
      vec.push(tuple3());
    }
    vec
  }

  pub fn list<T: FromStr>() -> Vec<T> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    buf.trim_right().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
  }

  pub fn lists<T: FromStr>(h: usize) -> Vec<Vec<T>> {
    let mut mat: Vec<Vec<T>> = vec![];
    for _ in 0 .. h {
      mat.push(list());
    }
    mat
  }

  pub fn chars() -> Vec<char> {
    let mut buf = String::new();
    let s = stdin();
    s.lock().read_line(&mut buf).ok();
    buf.trim_right().chars().collect()
  }
}

#[allow(dead_code)]
mod put {
  use std::string::*;

  pub fn vec<T: ToString>(vec: &Vec<T>, sep: &str) {
    let out = vec.iter().map(|e| e.to_string()).collect::<Vec<_>>().as_slice().join(sep);
    println!("{}", out);
  }

  pub fn mat<T: ToString>(mat: &Vec<Vec<T>>, sep: &str) {
    for v in mat {
      vec(v, sep);
    }
  }
}