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)

//************************
//*  Date: 2018.11.30    *
//*  Problem:            *
//*  Author: xuziyuan    * 
//************************
 
#include <bits/stdc++.h>
 
#define rt0 return 0
#define rep(i,n) for(int i=0;i<n;i++)
#define repn(i,n) for(int i=1;i<=n;i++)
#define replet(c) for(char c='a';c<='z';c++)
#define LL long long
#define pii pair<int,int>
#define pb push_back
#define fi first
#define se second
#define mpr make_pair
#define sqr(a) ((a)*(a))
 
using namespace std;
 
const LL MOD=1e9+7;
 
int n,m,q;
vector <int> g[100010];
int colo[100010],most[100010];
vector <pair<pii,int> > pa;
bool vis[100010];
 
int main()
{
	memset(most,-1,sizeof(most));
	cin>>n>>m;
	rep(i,m)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		g[x].pb(y);
		g[y].pb(x);
	}
	cin>>q;
	rep(i,q)
	{
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		pa.pb({{x,y},z});
	}
	for(int i=pa.size()-1;i>=0;i--)
	{
		int x=pa[i].fi.fi,y=pa[i].fi.se,z=pa[i].se;
		queue <pii> q;
		q.push({x,0});
		memset(vis,0,sizeof(vis));
		while(!q.empty())
		{
			int pos=q.front().fi,all=q.front().se;
			q.pop();
			if(y-all<=most[pos]) continue;
			most[pos]=y-all;
			if(all>y) continue;
			if(vis[pos]) continue;
			//if(x==1) cout<<pos<<endl;
			vis[pos]=true;
			if(colo[pos]==0) colo[pos]=z;
			rep(i,g[pos].size()) q.push({g[pos][i],all+1});
		}
	}
	repn(i,n) printf("%d\n",colo[i]);
	rt0;
}