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: Runtime Error)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#include<stack>
#include<queue>
#include<vector>
#include<algorithm>
#define max 2005
int color[max+1];
int distance[max+1][max+1];
int edge[max+1][max+1];
void bfs(int k,int n){
    int sumi[max];
    int i;
    for(i=1;i<=n;i++)sumi[i]=0;
    std::queue<int>q;
    q.push(k);
    sumi[k]=1;
    distance[k][k]=0;
    while(!q.empty()){
        int point=q.front();q.pop();
        for(i=1;i<=n;i++){
            if(sumi[i]==0){
                if(edge[point][i]==1){
                distance[k][i]=distance[k][point]+1;
                sumi[i]=1;
                q.push(i);
                }
            }
        }
    }
}
int main(){
    int n,m;
    scanf("%d %d",&n,&m);
    int i,j;
    for(i=1;i<=m;i++){
        int a,b;
        scanf("%d %d",&a,&b);
        edge[a][b]=1;
        edge[b][a]=1;
    }
    for(i=1;i<=n;i++)for(j=1;j<=n;j++)distance[i][j]=max+3;
    for(i=1;i<=n;i++){
        bfs(i,n);
    }
    int q;
    scanf("%d",&q);
    for(i=1;i<=q;i++){
        int v,d,c;
        scanf("%d %d %d",&v,&d,&c);
        for(j=1;j<=n;j++){
            if(distance[v][j]<=d){
                color[j]=c;
            }
        }
    }
    for(i=1;i<=n;i++){
        printf("%d\n",color[i]);
    }
    
    return 0;
}