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: Accepted)

var
  n,m,x,y,i,q,total:longint;
  b,p,d,v,tot,que,first,next,ans,c:array[0..200010]of longint;

procedure add(x,y:longint);
begin
    inc(total);
    next[total]:=first[x];
    first[x]:=total;
    b[total]:=y;
end;

procedure bfs(k:longint);
var
  head,tail:longint;
  s:longint;
begin
    head:=1;
    tail:=1;
    que[1]:=k;
    while head<=tail do begin
        s:=first[que[head]];
        if ans[que[head]]=0 then ans[que[head]]:=c[i];
        if tot[head]>p[que[head]] then begin
            p[que[head]]:=tot[head];
            if tot[head]>0 then begin
                while s<>-1 do begin
                    inc(tail);
                    tot[tail]:=tot[head]-1;
                    que[tail]:=b[s];
                    s:=next[s];
                end;
            end;
        end;
        inc(head);
    end;
end;

begin
    read(n,m);
    for i:=1 to n*2 do first[i]:=-1;
    for i:=1 to m do begin
        read(x,y);
        add(x,y);
        add(y,x);
    end;
    read(q);
    for i:=1 to q do read(v[i],d[i],c[i]);
    for i:=q downto 1 do begin
        if p[v[i]]>d[i] then continue;
        if (ans[v[i]]<>0)and(d[i]=0) then continue;
        tot[1]:=d[i];
        bfs(v[i]);
    end;
    for i:=1 to n do writeln(ans[i]);
end.