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 F first
#define S second
#define pii pair<int, int>
#define eb emplace_back
#define all(v) v.begin(), v.end()
#define rep(i, n) for (int i = 0; i < n; ++i)
#define rep3(i, l, n) for (int i = l; i < n; ++i)
#define max(a, b) (a > b ? a : b)
#define min(a, b) (a < b ? a : b)
#define chmax(a, b) a = (a >= b ? a : b)
#define chmin(a, b) a = (a <= b ? a : b)
#define out(a) cout << a << endl
#define outa(a, n) { rep(_, n) cout << a[_] << " "; cout << endl; }
#define outp(a, n) { cout << endl; rep(_, n) cout << a[_].F << " " << a[_].S << endl; }
#define SZ(v) (int)v.size()
#define inf (int)(1e9+7)
#define abs(x) (x >= 0 ? x : -(x))
#define ceil(a, b) a / b + !!(a % b)
#define FIX(a) fixed << setprecision(a)
#define LB(v, n) (int)(lower_bound(all(v), n) - v.begin())
#define UB(v, n) (int)(upper_bound(all(v), n) - v.begin())

ll n, m;
const int MAX_N = 100010;
vector<ll> g[MAX_N];
ll color[MAX_N];

// ある点のcolorが0でないからといってcontinueできない
// その先の頂点は別
// v, dのpairでメモ化
bool fin[MAX_N][11];

void dfs(ll v, ll d, ll c) {
    if (fin[v][d]) return;
    fin[v][d] = 1;
    if (d == 0) {
        color[v] = c;
        return;
    }
    dfs(v, d - 1, c);
    for (auto nxt : g[v]) {
        dfs(nxt, d - 1, c);
    }
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    
    cin >> n >> m;
    rep(i, m) {
        ll a, b;
        cin >> a >> b;
        a--; b--;
        g[a].eb(b);
        g[b].eb(a);
    }
    
    ll q;
    cin >> q;
    
    vector<ll> v(q), d(q), c(q);
    rep(i, q) cin >> v[q - 1 - i] >> d[q - 1 - i] >> c[q - 1 - i];
    
    // rep(i, q) cout << v[i] << " " << d[i] << " " << c[i] << endl;
    
    rep(i, q) {
        dfs(v[i] - 1, d[i], c[i]);
    }
    
    rep(i, n) out(color[i]);
}