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: Time Limit Exceeded)

#include<bits/stdc++.h>
#define N 201000
using namespace std;
void red(int &x)
{
	int f=1;x=0;char c=getchar();
	while(!isdigit(c)){if(c=='-')f=-1; c=getchar();}
	while(isdigit(c)){x=x*10+c-'0';c=getchar();}
	x*=f;
}
struct pu
{
	int id,w;
};
struct node
{
	int u,v,nxt;
}e[N<<1];
int first[N],cnt;
void ade(int u,int v)
{
	e[++cnt].nxt=first[u]; first[u]=cnt;
	e[cnt].u=u; e[cnt].v=v;
}
int n,m,q;
int v[N],d[N],c[N];
bool vis[N][15];
int ans[N];
bool check(int x,int d)
{
	for(int i=d+1;i<=11;i++)
		if(vis[x][i]) return 1;
	return 0;
}
void sol(int s,int d,int c)
{
	if(check(s,d)) return;
	queue<pu>q;
	q.push((pu){s,d}); vis[s][d]=1;
	while(!q.empty())
	{
		pu tmp=q.front(); q.pop();
		int u=tmp.id,w=tmp.w-1;
		if(!ans[u]) ans[u]=c;
		if(w==-1) continue;
		for(int i=first[u];i;i=e[i].nxt)
		{
			int v=e[i].v;
			if(check(v,w)) continue;
			vis[v][w]=1; q.push((pu){v,w});
		}
	}
}
int main()
{
//	scanf("%d%d",&n,&m);
	red(n);red(m);
	for(int i=1,a,b;i<=m;i++)
	{
	//	scanf("%d%d",&a,&b);
		red(a);red(b);
		ade(a,b); ade(b,a);
	}
	scanf("%d",&q);
	for(int i=1;i<=q;i++)
	//	scanf("%d%d%d",&v[i],&d[i],&c[i]);
		red(v[i]),red(d[i]),red(c[i]);
	for(int i=q;i>=1;i--)
		sol(v[i],d[i],c[i]);
	for(int i=1;i<=n;i++)
		printf("%d\n",ans[i]);
	return 0;
}