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: Time Limit Exceeded)

#include <bits/stdc++.h>
//#define Ak
 
using namespace std;
 
template< class t>
long long int gcd( t g,t h )
{
    return ( h==0 ? g : gcd(h,g%h) );
}
 
vector< int >v[100005];
int visit[100005]={0},color[100005]={0};
 
int dfs(int s,int d,int c)
{
    
    if(visit[s]==1)
    {
        return 0;
    }
    
    color[s]=c;
    
    if(d<=0)
    {
        return 0;
    }
    
    visit[s]=1;
    
    vector< int >::iterator k;
    
    for(k=v[s].begin();k!=v[s].end();k++)
    {
        if(visit[*k]==0)
        {
            color[*k]=c;
            dfs(*k,d-1,c);
        }
    }
    
    visit[s]=0;
    return 0;
    
}
 
 
int main()
{
   /* #ifdef Ak
    freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);
    #endif
    	
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    */
    int q,n,m,i,j,ans=0,sum=0,a,b,s,d,c;
    
   // list< long long int >v;
   
   // map< long long int >m;
   
    cin>>n>>m;
    
    for(i=0;i<m;i++)
    {
        cin>>a>>b;
        a--;
        b--;
        v[a].push_back(b);
        v[b].push_back(a);
    }
    
    cin>>q;
    
    while(q--)
    {
        cin>>s>>d>>c;
        s--;
        
        dfs(s,d,c);
        
    }
        
    for(i=0;i<n;i++)
    {
        cout<<color[i]<<endl;
    }
        
    return 0;
    
}