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: Time Limit Exceeded)

/*He who forgives and acknowledges himself... that is what it truly means to be strong!*/
#include <string>
#include <vector>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <stack>
#include <queue>
#include <cmath>
#include <algorithm>
#include <functional>
#include <list>
#include <deque>
#include <bitset>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <cstring>
#include <sstream>
#include <complex>
#include <iomanip>
#include <numeric>
#include <cassert>
#include <climits>
#include <utility>
#include <ctime>
#include <tuple>
#include <fstream>
#define T int test_case; scanf("%d",&test_case); while(test_case--)
#define FOR(i,a,n) for(i=a;i<n;i++)
#define FORD(i,a,n) for(i=a;i>=n;i--)
#define FORS(i,a) for(i=0;a[i];i++)
#define si(x) scanf("%d",&x)
#define sc(x) cin>>x
#define sd(x) scanf("%lf",&x)
#define sll(x) scanf("%lld",&x)
#define ss(x) scanf("%s",x)
#define prs(x) printf("%d ",x)
#define pls(x) printf("%lld ",x)
#define pc(x) printf("%c",x)
#define pi(x) printf("%d\n",x)
#define pd(x) cout.precision(10),cout<<fixed<<x<<endl;
#define pll(x) printf("%lld\n",x)
#define ps(x) printf("%s\n",x)
#define M 1000000007
#define ll long long
#define mp make_pair
#define all(x) x.begin(),x.end()
#define pb push_back
#define fr first
#define se second
#define in insert
#define er erase
#define pii pair<int, int>
#define plll pair<long long, long long>
#define tr(x,it) for(auto it : x)
#define INF 1ll<<60
#define PI 3.14159265358979323846264338327950288419716939937510582097494459230
#define bs(x,lo,hi,mid) cout<<x<<" "<<lo<<" "<<hi<<" "<<mid<<endl;
using namespace std;
ll gcd (ll a, ll b) {return ( a ? gcd(b%a, a) : b );}
ll power(ll a, ll n) {ll p = 1;while (n > 0) {if(n&1) {p = p * a;} n >>= 1; a *= a;} return p;}
ll power(ll a, ll n, ll mod) {ll p = 1;while (n > 0) {if(n&1) {p = p * a; p %= mod;} n >>= 1; a *= a; a %= mod;} return p % mod;}
vector<int> prime;
bool primee[10000000];
void primegen(ll x) { for(ll i=2;i*i<=x;i++) if(!primee[i]) for(ll j=i*i;j<=x;j+=i) primee[j]=true; for(ll i=2;i<=x;i++) if(!primee[i]) prime.push_back(i);}

const int N=100005;

vector<int> v[N];
int co[N];

void dfs(int s,int cd,int d,int c)
{
	co[s]=c;
	if(cd==d)
		return;
	int i;
	FOR(i,0,v[s].size())
		dfs(v[s][i],cd+1,d,c);
}

int main()
{
   int i,j;
   int n,m,q;
   si(n);
   si(m);
   int x,y;
   FOR(i,0,m)
   {
   	si(x);
   	si(y);
   	v[x].pb(y);
   	v[y].pb(x);
   }	
   int d,c;
   si(q);
   while(q--)
   {
   	si(x);
   	si(d);
   	si(c);
   	dfs(x,0,d,c);
   }
   FOR(i,1,n+1)
   	pi(co[i]);
   return 0;
}