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;
typedef long long ll;
const int N = 100500;
const int D = 12;

int dp[N][D];
int n, m, q;
vector <vector <int> > g;
int v[N], d[N], c[N];

void draw(int v, int d, int c)
{
	if (d == -1 || dp[v][d])
		return;

	dp[v][d] = c;


	for (int to : g[v])
		draw(to, d - 1, c);
}

int main()
{                                                     
	ios_base::sync_with_stdio(0);

	cin >> n >> m;

	g.resize(n);

	for (int i = 0; i < m; i++)
	{
		int a, b;
		cin >> a >> b;
		a--, b--;
		g[a].push_back(b);
		g[b].push_back(a);
	}

	cin >> q;

	for (int i = q - 1; i >= 0; i--)
	{
		cin >> v[i] >> d[i] >> c[i];
		v[i]--;
	}

	for (int i = 0; i < q; i++)
	{
		for (int x = d[i]; x >= 0; x--)
			draw(v[i], x, c[i]);
	}

	for (int i = 0; i < n; i++)
		cout << dp[i][0] << '\n';

	return 0;
}

