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 string $S = s_1s_2\ldots s_N$ 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 $4N$.

Input is given from Standard Input in the following format: >$N$ $M$\ >$u_1$ $v_1$\ >$u_2$ $v_2$\ >$\cdots$\ >$u_M$ $v_M$\ >$S$ #### 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 $1$.

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. >$K$\ >$A_1$ $A_2$ $\cdots$ $A_K$

***For Sample #1:*** The path $(2,5,6,5,6,3,1,3,6)$ has a length no greater than $4N$, and - it has odd number $(1)$ of $1$ - it has odd number $(1)$ of $2$ - it has even number $(2)$ of $3$ - it has even number $(0)$ of $4$ - it has even number $(2)$ of $5$ - it has odd number $(3)$ of $6$ so it is a good path with respect to $S=110001$. ***For Sample #2:*** An empty path $()$ is a good path with respect to $S=000000$. Alternatively, paths like $(1,2,3,1,2,3)$ are also accepted.

AtCoder [ABC244G]