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
def main():
    n, m = map(int, input().split())
    ab = [list(map(int, input().split())) for _ in [0]*m]
    q = int(input())
    vdc = [list(map(int, input().split())) for _ in [0]*q]

    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]

    dist = [[0]*11 for _ in [0]*n]
    dist2 = [0]*n

    for v, d, c in vdc[::-1]:
        v -= 1
        if dist[v][d] != 0:
            continue
        dist[v][d] = c
        if dist2[v] == 0:
            dist2[v] = c
        if d > 0:
            q = [(v, d, c)]
            while q:
                v, d, c = q.pop()
                for i in g[v]:
                    if dist[i][d-1] == 0:
                        dist[i][d-1] = c
                        if dist2[i] == 0:
                            dist2[i] = c
                        if d > 1:
                            q.append((i, d-1, c))
    for i in dist2:
        print(i)


main()
