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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#define FOR(i,a,n) for(int i=a;i<n;i++)
int g[2001][2001];
int size[100000];
int color[100000];
int visited[100000];
int c,d;
void dfs(int v,int n){
    color[v]=c;
    if(n==d) return;
    visited[v]=1;
    FOR(i,0,size[v]){
        if(!visited[g[v][i]]){
            dfs(g[v][i],n+1);
        }
    }
    visited[v]=0;
    return;
}
int main(void){
    int n,m,q;
    int a,b;
    int v;
    scanf("%d %d",&n,&m);
    FOR(i,0,m){
        scanf("%d %d",&a,&b);
        g[a][size[a]++]=b,g[b][size[b]++]=a;
    }
    scanf("%d",&q);
    FOR(i,0,q){
        scanf("%d %d %d",&v,&d,&c);
        dfs(v,0);
    }
    FOR(i,1,n+1) printf("%d\n",color[i]);
}