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)

#include <cstdio>
#include <algorithm>
#define maxn 100000+10
using namespace std;
int f[maxn],ans[maxn],n,m,Q,x,y,z,head[maxn],g;
struct xx
{
	int v,next;
}b[maxn<<1];

struct yy
{
	int x,d,col;
}a[maxn];

void add(int u,int v)
{
	b[++g]=(xx){v,head[u]};
	head[u]=g;
}

void dfs(int x,int d,int col)
{
	if (f[x]>=d) return ;
	f[x]=d;
	if (d<=0)return ;
	if (!ans[x])ans[x]=col;
	for (int i=head[x];i;i=b[i].next)
	{
		int v=b[i].v;
		dfs(v,d-1,col);
	}
}

int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i<=m;++i)
	  scanf("%d%d",&x,&y),add(x,y),add(y,x);
	scanf("%d",&Q);
	for (int i=1;i<=Q;++i)
	  scanf("%d%d%d",&x,&y,&z),a[i]=(yy){x,y+1,z};
	for (int i=Q;i>=1;--i)
	  dfs(a[i].x,a[i].d,a[i].col);
	for (int i=1;i<=n;++i) printf("%d\n",ans[i]);
	return 0;
}