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 <cstdio>
#include <cstring>
#include <vector>
#define N 100005 ////////////////////////////////////
using namespace std;

int n, m, Q, d[N], gi[N], di[N], num[N], ans[N];
vector<int> a[N];
void f(int p, int q, int w) {
	int i;
	if (d[p] >= q) return;
	d[p] = q;
	if (ans[p] == 0) ans[p] = w;
	for (i = 0; i < a[p].size(); i++) f(a[p][i], q - 1, w);
}
int main()
{
	int i, t1, t2;
	cin >> n >> m;
	while (m--) {
		scanf ("%d %d", &t1, &t2);
		a[t1].push_back(t2);
		a[t2].push_back(t1);
	}
	cin >> Q;
	for (i = 1; i <= Q; i++) {
		scanf ("%d %d %d", &gi[i], &di[i], &num[i]);
	}
	memset(d, -1, sizeof(d));
	for (i = Q; i >= 1; i--) {
		f(gi[i], di[i], num[i]);
	}
	for (i = 1; i<= n; i++) printf("%d\n", ans[i]);
    return 0;
}
