Problem Statement

You are given a simple connected undirected graph with $N$ vertices and $M$ edges. (A graph is said to be simple if it has no multi-edges and no self-loops.) For $i = 1, 2, \ldots, M$, the $i$-th edge connects Vertex $u_i$ and Vertex $v_i$.

A sequence $(A_1, A_2, \ldots, A_k)$ is said to be a path of length $k$ if both of the following two conditions are satisfied:

• For all $i = 1, 2, \dots, k$, it holds that $1 \leq A_i \leq N$.
• For all $i = 1, 2, \ldots, k-1$, Vertex $A_i$ and Vertex $A_{i+1}$ are directly connected with an edge.

An empty sequence is regarded as a path of length $0$.

You are given a sting $S = s_1s_2\ldots s_N$ of length $N$ consisting of $0$ and $1$. A path $A = (A_1, A_2, \ldots, A_k)$ is said to be a good path with respect to $S$ if the following conditions are satisfied:

• For all $i = 1, 2, \ldots, N$, it holds that:
• if $s_i = 0$, then $A$ has even number of $i$'s.
  • if $s_i = 1$, then $A$ has odd number of $i$'s.

Under the Constraints of this problem, it can be proved that there is at least one good path with respect to $S$ of length at most $4N$. Print a good path with respect to $S$ of length at most $4N$.

Constraints

• $2 \leq N \leq 10^5$
• $N-1 \leq M \leq \min\lbrace 2 \times 10^5, \frac{N(N-1)}{2}\rbrace$
• $1 \leq u_i, v_i \leq N$
• The given graph is simple and connected.
• $N, M, u_i$, and $v_i$ are integers.
• $S$ is a string of length $N$ consisting of $0$ and $1$.

Input

Input is given from Standard Input in the following format:

N M
u_1 v_1
u_2 v_2
\vdots
u_M v_M
S

Output

Print a good path with respect to $S$ of length at most $4N$ in the following format. Specifically, the first line should contain the length $K$ of the path, and the second line should contain the elements of the path, with spaces in between.

K
A_1 A_2 \ldots A_K