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 <iostream>
#include <vector>
#include <map>
#include <cstdio>
#include <cstring>
#include <math.h>
#include <bitset>
#include <time.h>
#include <set>
#include <algorithm>
#define MAXN 100000
#define MAXD 12

#define ll long long
using namespace std;

int N,M,Q;


int BFS[2][MAXN*MAXD+200];
bool done[(MAXN+100)*MAXD+200];
int colors[MAXN+200];

vector<int> edges[MAXN+2];

void doBFS(int u,int dist,int color) {
    BFS[0][0]=u*11+dist;
    int sz=1;
    
    for(int iters=1;sz>0;iters++) {
        int nsz=0;
        for(int j=0;j<sz;j++) {
            int curr = BFS[(iters-1)&1][j];
            

            int cu = curr/11;
            int cdist=curr%11;
            
            
            
            if (colors[cu]==-1)
                colors[cu]=color;


            if (done[cu*11+cdist])
                continue;
            
            for(int d=0;d<=cdist;d++)
                done[cu*11+cdist]=true;
            
            if (cdist==0)
                continue;


            for(int j=0;j<edges[cu].size();j++) {
                int v=edges[cu][j];

                if (done[v*11+cdist-1])
                    continue;

                BFS[iters&1][nsz++]=v*11+cdist-1;

            }
            
        }
        sz=nsz;
    }
    
}

int v[MAXN+2];
int dists[MAXN+2];
int splatter_colors[MAXN+2];

int main() {
    cin>>N>>M;
    
    
    for(int i=1;i<=M;i++) {
        int u,v;
        cin>>u>>v;
        edges[u].push_back(v);
        edges[v].push_back(u);
    }
    
    
    cin>>Q;
    
    v[0]=1;
    dists[0]=N+2;
    colors[0]=0;
    
    for(int i=1;i<=Q;i++) {
        cin>>v[i]>>dists[i]>>splatter_colors[i];
    }
    
    for(int i=1;i<=N;i++)
        colors[i]=-1;
    
    
    for(int i=0;i<=(N+2)*11+11;i++)
        done[i]=false;
    
    
    for(int q=Q;q>=0;q--) {
        doBFS(v[q],dists[q],splatter_colors[q]);
    }
    
    for(int i=1;i<=N;i++)
        if (colors[i]==-1)
            colors[i]=0;
    
    for(int i=1;i<=N;i++)
        printf("%d\n",colors[i]);
    

}