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>
#define MAX 15
#define N 100005
using namespace std;

int x,y,n,m,q,vv[N],d[N],c[N],color[N],dp[N][MAX];
vector<int> v[N];

void dfs(int node,int dist,int colo) {

  if(dp[node][dist]) return ;
  if(!color[node]) {
    color[node]=colo;
  }
  dp[node][dist]=1;
  if(!dist) return ;
  for(int i=0;i<v[node].size();i++) {
    dfs(v[node][i],dist-1,colo);
  }
  dfs(node,dist-1,colo);

}

int main() {

  scanf("%d %d",&n,&m);
  for(int i=1;i<=m;i++) {
    scanf("%d %d",&x,&y);
    v[x].push_back(y);
    v[y].push_back(x);
  }
  scanf("%d",&q);
  for(int i=1;i<=q;i++) {
    scanf("%d %d %d",&vv[i],&d[i],&c[i]);
  }
  for(int i=q;i>=1;i--) {
    dfs(vv[i],d[i],c[i]);
  }
  for(int i=1;i<=n;i++) {
    printf("%d\n",color[i]);
  }

}
