Given a tree of $n$ vertices rooted at $1$. Each vertice has a number, which is $0$ initially.

There are $q$ queries, they ask you, for every vertice on the simple path from $x$ to $y$, if the value on this vertice is $0$, assign $z$ to it. It is guaranteed that $x$ is an ancestor of $y$.

Find the number on each vertice after $q$ queries.

Input

• The first line contain 2 integers $n, q$.
• The next $n - 1$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$.
• The next $q$ lines, each line contains 3 integers $x, y, z$, a query.

Output

• Print $n$ integers, the $i^{th}$ number is number on vertice $i$.

Constraints

• $1 \le n, q, y \le 10^5$.
• $1 \le u, v, x \le n$.

Example

Input:

5 3
1 2
2 3
2 4
1 5
1 3 1
1 4 2
1 2 3

Output:

1 1 1 2 0