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;

#define fi first
#define se second

typedef pair<int ,int> pii;
typedef pair<int ,pii> pipii;

int N,M,Q;
int dp[100010][20] = {0};
pipii que[100010];
int ans[100010] = {0};
vector<int> V[100010];

void drow(int v,int d,int c)
{
    if(dp[v][d] != 0)return;
    dp[v][d] = 1;
    if(ans[v] == 0)ans[v] = c;
    if(d == 1)return;
    for(int i = 0; i < V[v].size(); i++)
    {
        drow(V[v][i],d - 1,c);
    }
    return;
}

int main()
{
    scanf("%d%d",&N,&M);
    for(int i = 0; i < M; i++)
    {
        int a,b;
        scanf("%d%d",&a,&b);
        V[a].push_back(b);
        V[b].push_back(a);
    }
    scanf("%d",&Q);
    for(int i = 0; i < Q; i++)
    {
        scanf("%d%d%d",&que[Q - i - 1].fi ,&que[Q - i - 1].se.fi ,&que[Q - i - 1].se.se);
    }
    for(int i = 0; i < Q; i++)
    {
        int v,d,c;
        v = que[i].fi;d = que[i].se.fi;c = que[i].se.se;
        drow(v,d + 1,c);
    }
    for(int i = 1; i < N + 1; i++)printf("%d\n",ans[i]);
    return 0;
}