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;
typedef long long ll;
#define mk make_pair
#define pb push_back
#define pf push_front
typedef pair<int, int> pii;
const int mod = 1000000007;
const int INF = 1000000009;
const long long INFL = 1000000000000000018ll;

int N, M, Q;
int v[100100], d[100100], c[100100];
int dp[100100][11];
int col[100100];
vector<int> G[100100];

void dfs(int V, int D, int C)
{
    if(~dp[V][D]){
        return;
    }
    dp[V][D] = 0;
    if(col[V] == 0){
        col[V] = C;
    }
    if(D == 0)return;
    for(int i = 0; i < (int)G[V].size(); i++){
        int to = G[V][i];
        dfs(to, D - 1, C);
    }
    return;
}

signed main()
{
    cin >> N >> M;
    for(int i = 0; i < M; i++){
        int a, b;
        cin >> a >> b;
        a--;
        b--;
        G[a].pb(b);
        G[b].pb(a);
    }
    memset(dp, -1, sizeof(dp));
    cin >> Q;
    for(int i = 0; i < Q; i++){
        cin >> v[i] >> d[i] >> c[i];
    }
    for(int i = Q - 1; i >= 0; i--){
        v[i]--;
        dfs(v[i], d[i], c[i]);
    }
    for(int i = 0; i < N; i++){
        printf("%d\n", col[i]);
    }



    return 0;
}