Problem Statement

You are given a connected undirected graph $G$ with $N$ vertices and $M$ edges. For each $i=1,2,\ldots,M$, the $i$-th edge connects vertices $a_i$ and $b_i$, and is colored red if $c_i=$ R and blue if $c_i=$ B.

Determine if there is a spanning tree of $G$ that satisfies the following condition, and if so, display such a tree.

• For every $i=1,2,\ldots,N$,
• if $s_i =$ R, at least one red edge has vertex $i$ as its endpoint;
  • if $s_i =$ B, at least one blue edge has vertex $i$ as its endpoint.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $N-1 \leq M \leq 2 \times 10^5$
• $1 \leq a_i \lt b_i \leq N$
• $c_i$ is R or B.
• $(a_i,b_i,c_i) \neq (a_j,b_j,c_j)$ if $i \neq j$.
• The given graph is connected.
• $s_i$ is R or B.
• $N,M,a_i,b_i$ are integers.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
\vdots
a_M b_M c_M
s_1 s_2 \ldots s_N

Output

If no spanning tree of $G$ satisfies the condition, print No.

No

Otherwise, print such a tree in the following format:

Yes
t_1 t_2 \ldots t_{N-1}

This means that the $i$-th edge of the spanning tree is the $t_i$-th edge of $G$. If multiple spanning trees of $G$ satisfy the condition, any one of them is accepted.