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<bits/stdc++.h>
int p[100010],d[100010],c[100010],n,m,q;
int to[200010],nxt[200010],fst[100010],tot;
void add(int u,int v)
{
    to[++tot]=v;
    nxt[tot]=fst[u];
    fst[u]=tot;
}
int a[100010];
bool vis[100010][11];
void color(int p,int d,int c)
{
    if(vis[p][d]||d<0)return;
    vis[p][d]=1;if(!a[p])a[p]=c;
    for(int e=fst[p];e;e=nxt[e])
        color(to[e],d-1,c);
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1,u,v;i<=m;++i)
    {
        scanf("%d%d",&u,&v);
        add(u,v),add(v,u);
    }
    scanf("%d",&q);
    for(int i=1;i<=q;++i)
        scanf("%d%d%d",&p[i],&d[i],&c[i]);
    for(int i=q;i;--i)color(p[i],d[i],c[i]);
    for(int i=1;i<=n;++i)printf("%d\n",a[i]);
    return 0;
}
