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;
typedef unsigned long long ull;
int inf_int=1e9;
ll inf_ll=1e16;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define pb push_back
const double pi=3.1415926535898;
#define dout if(debug) cout
#define fi first
#define se second
#define sp setprecision
#define siz(a) a.size()
#define EPS 1e-7
#define next asdfafgasgasg
bool debug=0;
typedef long double dbl;
const int MAXN = 2e5;
const int MOD = 1e9 +7;



vector<int> g[MAXN];
pii val[MAXN][11];
void solve()
{
    int n;
    cin >> n;
    int m;
    cin >> m;
    for(int i=1;i<=m;++i){
        int a,b;
        cin >> a >> b;
        g[a].pb(b);
        g[b].pb(a);
    }

    int q;
    cin >> q;
    for(int j=1;j<=q;++j){
        int d,v,c;
        cin >> v >> d >> c ;
        val[v][d]={j,c};
    }

    for(int d=10;d>=1;d--){
        for(int v=1;v<=n;v++){
            for(int to:g[v]){
                val[to][d-1]=max(val[to][d-1],val[v][d]);
            }
            val[v][d-1]=max(val[v][d-1],val[v][d]);
        }

    }

    for(int i=1;i<=n;++i){
        if(i>1){
            cout <<"\n";
        }
        cout << val[i][0].se;

    }
    cout <<"\n";

}


#define FILE "palindrome"
int main()
{
        #ifdef zxc
            freopen("input.txt","r",stdin);
 //          freopen("output.txt","w",stdout);
        #else
         //     freopen(FILE".in","r",stdin);
         //     freopen(FILE".out","w",stdout);
        #endif // zxc

     //  freopen(FILE".in","r",stdin);
     //   freopen(FILE".out","w",stdout);

     //   freopen("input.txt","r",stdin);
       // freopen("output.txt","w",stdout);

       if(!debug)
       {
            ios_base::sync_with_stdio(0);
            cin.tie(0);
            cout.tie(0);
       }

        int t=1;
        while(t--)
           solve();
        return 0;
}