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>
#include<cstring>
#define INF 0x3f3f3f3f
#define maxn 100005
int n,m,q,s[maxn],d[maxn],x[maxn],maxd[maxn],c[maxn],que[maxn],fr,bk;
struct node { int v; node *nxt; } edge[maxn*2],*head[maxn],*ncnt;
void addedge(int u,int v)
{
	ncnt++;
	ncnt->v=v,ncnt->nxt=head[u];
	head[u]=ncnt;
}
void dfs(int u,int d,int x)
{
	if(maxd[u]>=d) return;
	if(!c[u]) c[u]=x;
	if(!d) return;
	maxd[u]=d;
	for(node *p=head[u];p;p=p->nxt) dfs(p->v,d-1,x);
}
int main()
{
	scanf("%d%d",&n,&m);
	ncnt=&edge[0];
	for(int i=1;i<=m;i++)
	{
		int u,v;
		scanf("%d%d",&u,&v);
		addedge(u,v); addedge(v,u);
	}
	memset(maxd,-1,sizeof(maxd));
	scanf("%d",&q);
	for(int i=1;i<=q;i++) scanf("%d%d%d",&s[i],&d[i],&x[i]);
	for(int i=q;i;i--) dfs(s[i],d[i],x[i]); 
	for(int i=1;i<=n;i++) printf("%d\n",c[i]);
}