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 (Clang 3.8.0) (judge verdict: Accepted)

//
//  main.cpp
//

#include <algorithm>
#include <array>
#include <assert.h>
#include <complex>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <memory>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

using ll = int64_t;
using ull = uint64_t;
constexpr ll LL_MAX = numeric_limits<ll>::max();
constexpr ull ULL_MAX = numeric_limits<ull>::max();

template<typename T>
vector<T> make_vec_nd(T init, ll size) {
    return vector<T>(size, init);
}
template<typename T, typename... Args>
auto make_vec_nd(T init, ll size, Args... rest) {
    auto inner = make_vec_nd(init, rest...);
    return vector<decltype(inner)>(size, inner);
}

#define rep(i, a, b) for (ll i = (a); i < (b); i++)
#define rrep(i, a, b) for (ll i = (a)-1; i >= (b); i--)

int main() {
    ll N, M;
    cin >> N >> M;
    struct Edge {
        ll from;
        ll to;
    };
    vector<Edge> edges;
    rep(i,0,M) {
        ll a, b;
        cin >> a >> b;
        a--;
        b--;
        edges.push_back(Edge{a, b});
        edges.push_back(Edge{b, a});
    }
    ll Q;
    cin >> Q;
    struct Query {
        ll v;
        ll d;
        ll c;
    };
    vector<Query> queries(Q);
    rep(q,0,Q) {
        ll v, d, c;
        cin >> v >> d >> c;
        v--;
        queries[q] = {v, d, c};
    }
    struct Data {
        ll p; // priority
        ll c; // color
        void add(const Data& rhs) {
            if (rhs.p > p) {
                *this = rhs;
            }
        }
    };
    vector<vector<Data>> data(N);
    rep(i,0,N) {
        data[i] = vector<Data>(11, Data{-1, 0});
    }
    rep(i,0,Q) {
        Query q = queries[i];
        data[q.v][q.d].add(Data{i, q.c});
    }
    rep(loop,0,11) {
        for (Edge& e : edges) {
            rep(d,1,11) {
                data[e.to][d-1].add(data[e.from][d]);
            }
        }
    }
    rep(i,0,N) {
        Data ans{-1, 0};
        rep(d,0,11) {
            ans.add(data[i][d]);
        }
        cout << ans.c << endl;
    }
}