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.

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.

Examples

Input

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2


Output

2
2
2
2
2
1
0


Input

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


Output

1
0
3
1
5
5
3
3
6
1
3
4
5
3
#include <cstdio> 
#define For(x) for (int h=head[x],o=V[h]; h; o=V[h=to[h]])
#define add(u,v) (to[++num]=head[u],head[u]=num,V[num]=v)
int num,head[100005],to[200005],V[200005];
int Q,n,m,v[100005],d[100005],c[100005],cl[100005],rg[100005];

void dfs(int x,int ran,int col){
	if (rg[x]>=ran || ran<=0) return;
	rg[x]=ran;
	if (!cl[x]) cl[x]=col;
	For(x) dfs(o,ran-1,col);
}

int main(){
	scanf("%d%d",&n,&m);
	for (int i=1,x,y; i<=m; i++){
		scanf("%d%d",&x,&y);
		add(x,y); add(y,x);
	}
	scanf("%d",&Q);
	for (int i=1; i<=Q; i++) scanf("%d%d%d",&v[i],&d[i],&c[i]);	
	for (int i=Q; i; i--) dfs(v[i],d[i]+1,c[i]);
	for (int i=1; i<=n; i++) printf("%d\n",cl[i]);
}

//http://agc012.contest.atcoder.jp/tasks/agc012_b