You are given a tree consisting of $n$ vertices, and $q$ triples $(x_i, y_i, s_i)$, where $x_i$ and $y_i$ are integers from $1$ to $n$, and $s_i$ is a string with length equal to the number of vertices on the simple path from $x_i$ to $y_i$.

You want to write a lowercase Latin letter on each vertex in such a way that, for each of $q$ given triples, at least one of the following conditions holds:

• if you write out the letters on the vertices on the simple path from $x_i$ to $y_i$ in the order they appear on this path, you get the string $s_i$;
• if you write out the letters on the vertices on the simple path from $y_i$ to $x_i$ in the order they appear on this path, you get the string $s_i$.

Find any possible way to write a letter on each vertex to meet these constraints, or report that it is impossible.

Input

The first line contains two integers $n$ and $q$ ($2 \le n \le 4 \cdot 10^5$; $1 \le q \le 4 \cdot 10^5$) — the number of vertices in the tree and the number of triples, respectively.

Then $n - 1$ lines follow; the $i$-th of them contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$; $u_i \ne v_i$) — the endpoints of the $i$-th edge. These edges form a tree.

Then $q$ lines follow; the $j$-th of them contains two integers $x_j$ and $y_j$, and a string $s_j$ consisting of lowercase Latin letters. The length of $s_j$ is equal to the number of vertices on the simple path between $x_j$ and $y_j$.

Additional constraint on the input: $\sum \limits_{j=1}^{q} |s_j| \le 4 \cdot 10^5$.

Output

If there is no way to meet the conditions on all triples, print NO. Otherwise, print YES in the first line, and a string of $n$ lowercase Latin letters in the second line; the $i$-th character of the string should be the letter you write on the $i$-th vertex. If there are multiple answers, print any of them.

见题面 Input 部分

见题面 Output 部分