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 Pascal (FPC 2.6.2) (judge verdict: Time Limit Exceeded)

var i,j,k,l,m,n,q,w,x,y,t:longint;
    st,ed,first,next,d,v,color,fw,c:array[1..200000] of longint;
    b:array[1..200000]of boolean;
procedure ad(p,o:longint);
begin
    t:=t+1;  ed[t]:=o; next[t]:=first[p];first[p]:=t;
end;
procedure dfs(p,o,cl:longint);
var i,j:longint;
begin
    if fw[p]>o then exit;
    i:=first[p]; fw[p]:=o;  b[p]:=true;
    if color[p]=0 then color[p]:=cl;
    while (i>=1) do begin
        if b[ed[i]]=false then
               dfs(ed[i],o-1,cl);
        i:=next[i];
    end;
   b[p]:=false;
end;
begin
    readln(n,m);
    for i:=1 to m do first[i]:=-1;
    for i:=1 to m do begin readln(x,y); ad(x,y);ad(y,x); end;
    readln(q);
    for i:=1 to q do readln(v[i],d[i],c[i]);
    for i:=q downto 1 do begin dfs(v[i],d[i],c[i]); end;
    for i:=1 to n do writeln(color[i]);
end.