Problem:
Score : 700 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the testset satisfying 1 ≤ N,M,Q ≤ 2{,}000.

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.

Sample Input 1

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2

Sample Output 1

2
2
2
2
2
1
0

Initially, each vertex is painted in color 0.
In the first operation, vertices 5 and 6 are repainted in color 1.
In the second operation, vertices 1, 2, 3, 4 and 5 are repainted in color 2.

Sample Input 2

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

Sample Output 2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

template <typename T> inline void rd(T& x) {
	int si = 1; char c = getchar(); x = 0;
	while(!isdigit(c)) si = c == '-' ? -1 : si, c = getchar();
	while(isdigit(c)) x = x * 10 + c - 48, c = getchar();
	x *= si;
}
template <typename T, typename... Args>
inline void rd(T& x, Args&... args) { rd(x); rd(args...); }

#define fi first
#define se second

typedef long long ll;
typedef double ff;
typedef std::pair<int, int> pii;

const int kN = 1e5 + 5, kD = 12;

int n, m, c[kN], t[kN][kD];
std::vector <int> E[kN];

int main() {
	rd(n, m);
	for(int i = 1; i <= m; ++i) {
		int x, y; rd(x, y);
		E[x].push_back(y); E[y].push_back(x);
	}
	int q; rd(q);
	for(int i = 1; i <= q; ++i) {
		int v, d; rd(v, d, c[i]);
		t[v][d] = i;
	}
	for(int k = 1; k <= 10; ++k) 
		for(int i = 1; i <= n; ++i)
			for(auto v : E[i])
				for(int j = 0; j < 10; ++j)
					t[v][j] = std::max(t[i][j + 1], t[v][j]);
	for(int i = 1; i <= n; ++i) {
		int x = 0;
		for(int j = 0; j <= 10; ++j) x = std::max(x, t[i][j]);
		printf("%d\n", c[x]);
	}
	return 0;
}