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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define fr first
#define sc second
using namespace std;

const int mnx = 1e6 + 9;
const int mod =  1e9 + 7;

ll n, m, q, cl[mnx], v[mnx], d[mnx], c[mnx], r[mnx];
vector<int> g[mnx];

void funk(int v, int d, int c){
    if(d < 0) return;
    if(cl[v] == 0) cl[v] = c;
    if(r[v] < d){
        r[v] = d;
        for(int to : g[v]){
            funk(to, d - 1, c);
        }
    }
}

int main(){

cin >> n >> m;

for(int i = 0, v, u; i < m; i++){
    cin >> v >> u;
    g[v].pb(u);
    g[u].pb(v);
}

cin >> q;

for(int i = 1; i <= q; i++){
    cin >> v[i] >> d[i] >> c[i];
}

for(int i = q; i >= 1; --i){
    funk(v[i], d[i], c[i]);
    r[v[i]] = d[i];
}

for(int i = 1; i <= n; i++){
    cout << cl[i] << '\n';
}

return 0;

}