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: Wrong Answer)

type arr=array[1..200000]of longint;
var n,q,m,i,j,a,b:longint;
    v,d,c,max,cl,head,next,start,endd:arr;
    bb,bc:array[1..100000]of boolean;
procedure dfs(k,dis,col:longint);
var i:longint;
begin
    bb[k]:=true;
    if(max[k]>=dis)and(bc[k])then exit;
    max[k]:=dis;
    if not bc[k]then begin
        cl[k]:=col;
        bc[k]:=true;
    end;
    if dis>0 then for i:=start[k] to endd[k] do
    if not bb[next[i]]then dfs(next[i],dis-1,col);
    bb[k]:=false;
end;
procedure sort(l,r:longint);
var i,j,x,y:longint;
begin
    i:=l;j:=r;x:=head[(l+r) div 2];
    repeat
        while head[i]<x do inc(i);
        while x<head[j] do dec(j);
        if not(i>j) then begin
            y:=head[i];head[i]:=head[j];head[j]:=y;
            y:=next[i];next[i]:=next[j];next[j]:=y;
            inc(i);j:=j-1;
        end;
    until i>j;
    if l<j then sort(l,j);
    if i<r then sort(i,r);
end;
begin
    readln(n,m);
    fillchar(cl,sizeof(cl),0);
    fillchar(max,sizeof(max),0);
    fillchar(bb,sizeof(bb),false);
    fillchar(bc,sizeof(bc),false);
    for i:=1 to m do begin
        readln(a,b);
        head[i]:=a;head[i+m]:=b;
        next[i]:=b;next[i+m]:=a;
    end;
    m:=m*2;sort(1,m);start[head[1]]:=1;
    for i:=2 to m do if head[i]<>head[i-1]then begin
        endd[head[i-1]]:=i-1;
        start[head[i]]:=i;
    end;
    endd[head[m]]:=m;
    readln(q);
    for i:=q downto 1 do readln(v[i],d[i],c[i]);
    for i:=1 to q do dfs(v[i],d[i],c[i]);
    for i:=1 to n do writeln(cl[i]);
end.