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;
vector<int> e[100001];
int n,m,q,mp[100001],han[100001];

typedef pair<int,int> P;
void bfs(int p,int c,int d){
  queue<P> q;
  q.push(P(p,0));
  while(!q.empty()){
    P tp=q.front();q.pop();
    if(tp.second==d+1)break;
    if(han[tp.first]>=d-tp.second)continue;
    if(!mp[tp.first])mp[tp.first]=c;
    han[tp.first]=d-tp.second;
    for(int i=0;i<e[tp.first].size();i++)
      q.push(P(e[tp.first][i],tp.second+1));
  }
}
int main(){
  cin>>n>>m;
  for(int i=0,a,b;i<m;i++){
    cin>>a>>b;
    e[a].push_back(b);
    e[b].push_back(a);
  }
  cin>>q;
  int v[100001],d[100001],c[100001];
  for(int i=0;i<q;i++)
    cin>>v[i]>>d[i]>>c[i];
  memset(han,-1,sizeof(han));
  for(int i=q-1;i>=0;i--)
    bfs(v[i],c[i],d[i]);
  
  for(int i=1;i<=n;i++)cout<<mp[i]<<endl;
  return 0;
}
