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>
using namespace std;
using ll = long long;
#define FOR(i, a, b) for (int i = (a); i < int(b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= int(a); --i)
#define rep(i, n) FOR(i, 0, n)
#define rep1(i, n) FOR(i, 1, int(n) + 1)
#define rrep(i, n) RFOR(i, 0, n)
#define rrep1(i, n) RFOR(i, 1, int(n) + 1)
#define all(c) begin(c), end(c)
const int MOD = 1000000007;

template <typename T>
void __dump__(std::ostream &os, const T &first) {
    os << first;
}
template <typename First, typename... Rest>
void __dump__(std::ostream &os, const First &first, const Rest &... rest) {
    os << first << ", ";
    __dump__(os, rest...);
}
#define dump(...)                                         \
    do {                                                  \
        std::ostringstream os;                            \
        os << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; \
        __dump__(os, __VA_ARGS__);                        \
        std::cerr << os.str() << std::endl;               \
    } while (0)

using Weight = int;
using Flow = int;
struct Edge {
    int src, dst;
    Weight weight;
    Flow cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {}
};
using Edges = std::vector<Edge>;
using Graph = std::vector<Edges>;
using Array = std::vector<Weight>;
using Matrix = std::vector<Array>;

void add_edge(Graph &g, int a, int b, Weight w = 1) {
    g[a].emplace_back(a, b, w);
    g[b].emplace_back(b, a, w);
}
void add_arc(Graph &g, int a, int b, Weight w = 1) { g[a].emplace_back(a, b, w); }

int n, m;
Graph g;
int q;

pair<int,int> time_color[11][100010]; // dist, vertex -> time, color

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    while(cin >> n >> m && n){
        g.assign(n, {});
        rep(i, m){
            int a, b;
            cin >> a >> b;
            --a; --b;
            add_edge(g, a, b);
        }
        rep(i, n) {
            add_edge(g, i, i);
        }

        rep(i, 11) rep(j, n) time_color[i][j] = {0, 0};
        cin >> q;
        rep(t, q){
            int v, d, c;
            cin >> v >> d >> c;
            --v;
            time_color[d][v] = make_pair(t + 1, c);
        }

        rrep1(d, 10) {
            rep(v, n) {
                for (auto &e : g[v]) {
                    int w = e.dst;
                    if (time_color[d-1][w] < time_color[d][v]) {
                        time_color[d-1][w] = time_color[d][v];
                    }
                }
            }
        }
        rep(i, n){
            auto res = make_pair(0, 0);
            rep(j, 11){
                res = max(res, time_color[j][i]);
            }
            cout << res.second << '\n';
        }
    }
}