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 N = 300001;
int n, m, tot = 0, q;
int head[N], Next[N], ver[N], num[N];
int ans[N][20] = {};
struct edge{
	int x, y, z;
}a[N];

vector <int> vis[N];

void dfs(int x,int y,int z) {
	if (y == -1) return;
	if (ans[x][y]) return;
	ans[x][y] = z;
	for (int i=0;i<vis[x].size();++i) dfs(vis[x][i], y-1, z);
}

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