Problem Statement

We have a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered as Vertex $1$, Vertex $2$, $\dots$, Vertex $N$. The edges are numbered as Edge $1$, Edge $2$, $\dots$, Edge $M$. Edge $i$ connects Vertex $a_i$ and Vertex $b_i$ bidirectionally. There is no edge that directly connects Vertex $1$ and Vertex $N$. Each vertex is either empty or occupied by a wall. Initially, every vertex is empty.

Aoki is going to travel from Vertex $1$ to Vertex $N$ along the edges on the graph. However, Aoki is not allowed to move to a vertex occupied by a wall.

Takahashi has decided to choose some of the vertices to build walls on, so that Aoki cannot travel to Vertex $N$ no matter which route he takes. Building a wall on Vertex $i$ costs Takahashi $c_i$ yen (the currency of Japan). He cannot build a wall on Vertex $1$ and Vertex $N$.

How many yens is required for Takahashi to build walls so that the conditions is satisfied? Also, print the way of building walls to achieve the minimum cost.

Constraints

• $3 \leq N \leq 100$
• $N - 1 \leq M \leq \frac{N(N-1)}{2} - 1$
• $1 \leq a_i \lt b_i \leq N$ $(1 \leq i \leq M)$
• $(a_i, b_i) \neq (1, N)$
• The given graph is simple and connected.
• $1 \leq c_{i} \leq 10^9$ $(2 \leq i \leq N-1)$
• $c_1 = c_N = 0$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
\vdots
a_M b_M
c_1 c_2 \dots c_N

Output

Print in the following format. Here, $C,k$, and $p_i$ are defined as follows.

• $C$ is the cost that Takahashi will pay
• $k$ is the number of vertices for Takahashi to build walls on
• $(p_1,p_2,\dots,p_k)$ is a sequence of vertices on which Takahashi will build walls

C
k
p_1 p_2 \dots p_k

If there are multiple ways to build walls to satisfy the conditions with the minimum cost, print any of them.