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 FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define RFOR(i,b,a) for (int i = (b)-1; i >= (a); --i)
#define ITER(it,a) for (__typeof(a.begin()) it = a.begin(); it != a.end(); it++)
#define FILL(a,value) memset(a, value, sizeof(a))

#define SZ(a) (int)a.size()
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;

const double PI = acos(-1.0);
const int INF = 1000 * 1000 * 1000 + 7;
const LL LINF = 1LL * INF * INF;

const int MAX = 100100;

vector<PII> g[MAX];
int C[MAX];
pair<int,PII> Q[MAX];

int us[MAX];

int ID = 1;

int done = 0;
int n;

PII q[MAX];
int qt,qh;
void paint(int v,int d,int c)
{
	if(done== n)return;
	ID++;
	qt=qh=0;
	q[qt++]=(MP(v,d));
	us[v]=ID;
	if(C[v] == 0)C[v] = c,++done;
	while(qh!=qt)
	{
		int v = q[qh].first;
		int d = q[qh].second;
//		cerr<<v<<" "<<d<<" "<<c<<" "<<C[v]<<endl;
		++qh;
		if(d==0)continue;

		FOR(i,0,SZ(g[v]))
		{
			int to = g[v][i].first;
			int ds = g[v][i].second;
			if(ds>=d)continue;
			if(us[to]==ID)continue;
			g[v][i].second = d;
			if(C[to]==0)
			{
				C[to]=c;
				++done;
				if(done == n)return;
			}
			us[to]=ID;
			if(d==1)continue;

			q[qt++]=(MP(to,d-1));
		}
	}
}
int main()
{
	//freopen("in.txt", "r", stdin);
	//ios::sync_with_stdio(false); cin.tie(0);

	int m;

	scanf("%d%d",&n,&m);

	FOR(i,0,m)
	{
		int a,b;
		scanf("%d%d",&a,&b);
		--a;--b;
		g[a].PB(MP(b,0));
		g[b].PB(MP(a,0));
	}

	int q;
	scanf("%d",&q);
	FOR(i,0,q)
	{
		scanf("%d%d%d",&Q[i].first,&Q[i].second.first,&Q[i].second.second);
		--Q[i].first;
	}

	RFOR(i,q,0)
	{
		paint(Q[i].first,Q[i].second.first,Q[i].second.second);
	}

	FOR(i,0,n)
	{
		printf("%d\n",C[i]);
	}
}