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 <iostream>
#include <algorithm>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
int n,m,q,i,j,vis[100005],col[100005],cen[100005],dis[100005],c[100005],x,y;
vector<int> bi[100005];
void dfs(int x,int y,int z)
{
	if (vis[x]>=y) return;
	vis[x]=y;
	if (!col[x]) col[x]=z; 
	int i;
	for (i=0;i<bi[x].size();i++)
	{
		dfs(bi[x][i],y-1,z);
	}
}
int main()
{
	ios_base::sync_with_stdio(0);
	cin>>n>>m;
	for (i=1;i<=m;i++)
	{
		cin>>x>>y;
		bi[x].push_back(y);
		bi[y].push_back(x);
	}
	cin>>q;
	for (i=1;i<=q;i++) cin>>cen[i]>>dis[i]>>c[i];
	for (i=q;i>0;i--)
	{
		dfs(cen[i],dis[i]+1,c[i]);
	}
	for (i=1;i<=n;i++) cout<<col[i]<<endl;
	return 0;
}