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.

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.

Examples

Input

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2


Output

2
2
2
2
2
1
0


Input

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


Output

1
0
3
1
5
5
3
3
6
1
3
4
5
3
#include <bits/stdc++.h>
using namespace std;
const int maxn=100005;
struct QES{
	int v,d,c;
	QES(){}
	QES(int x,int y,int z){v=x;d=y;c=z;}
}qes[maxn];
int n,m,q,vis[maxn],col[maxn];
vector<int> eg[maxn];
void dfs(QES nd){
	if(col[nd.v]==0) col[nd.v]=nd.c;
	if(nd.d==0) return;
	for(int i=0;i<eg[nd.v].size();i++){
		if(vis[eg[nd.v][i]]<nd.d-1){
			vis[eg[nd.v][i]]=nd.d-1;
			dfs(QES(eg[nd.v][i],nd.d-1,nd.c));
		}
	}
}
int main(){
	int t1,t2;
	scanf("%d%d",&n,&m);
	for(int i=0;i<m;i++){
		scanf("%d%d",&t1,&t2);
		eg[t1].push_back(t2);
		eg[t2].push_back(t1);
	}
	scanf("%d",&q);
	for(int i=0;i<q;i++) scanf("%d%d%d",&qes[i].v,&qes[i].d,&qes[i].c);
	memset(vis,-1,sizeof(vis));
	for(int i=q-1;i>=0;i--){
		if(vis[qes[i].v]<qes[i].d){
			vis[qes[i].v]=qes[i].d;
			dfs(qes[i]);
		}
	}
	for(int i=1;i<=n;i++) printf("%d\n",col[i]);
	return 0;
}