For problem statement at 0-999/900-999/920-929/925/problemD.txt this is a correct solution, but verifier at 0-999/900-999/920-929/925/verifierD.go ends with wrong answer on test 11
input:
 4 2
1 2
1 3

expected:
 -1

got:
 3
1 2 3 4 


exit status 1 can you fix the verifier? ```go
package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

type State struct {
	u, k int
}

type DList struct {
	head       int
	next, prev []int
}

func newDList(n int) *DList {
	return &DList{
		head: 0,
		next: make([]int, n+1),
		prev: make([]int, n+1),
	}
}

func (l *DList) push(x int) {
	if l.head != 0 {
		l.prev[l.head] = x
	}
	l.next[x] = l.head
	l.prev[x] = 0
	l.head = x
}

func (l *DList) remove(x int) {
	p := l.prev[x]
	n := l.next[x]
	if p != 0 {
		l.next[p] = n
	} else {
		l.head = n
	}
	if n != 0 {
		l.prev[n] = p
	}
	l.next[x] = 0
	l.prev[x] = 0
}

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Buffer(make([]byte, 1024*1024), 1024*1024*10)
	scanner.Split(bufio.ScanWords)

	if !scanner.Scan() {
		return
	}
	n, _ := strconv.Atoi(scanner.Text())
	scanner.Scan()
	m, _ := strconv.Atoi(scanner.Text())

	adj := make([][]int, n+1)
	for i := 0; i < m; i++ {
		scanner.Scan()
		u, _ := strconv.Atoi(scanner.Text())
		scanner.Scan()
		v, _ := strconv.Atoi(scanner.Text())
		adj[u] = append(adj[u], v)
		adj[v] = append(adj[v], u)
	}

	dist := make([][2]int, n+1)
	parent := make([][2]State, n+1)
	for i := 1; i <= n; i++ {
		dist[i][0] = -1
		dist[i][1] = -1
	}
	dist[1][0] = 0

	S0 := newDList(n)
	S1 := newDList(n)
	inS0 := make([]bool, n+1)
	inS1 := make([]bool, n+1)

	for i := 2; i <= n; i++ {
		S0.push(i)
		inS0[i] = true
	}
	S1.push(1)
	inS1[1] = true

	isOpen := make([]bool, n+1)
	queue := make([]State, 0, 2*n)
	queue = append(queue, State{u: 1, k: 0})

	for len(queue) > 0 {
		curr := queue[0]
		queue = queue[1:]
		u := curr.u
		K := curr.k

		for _, v := range adj[u] {
			isOpen[v] = true
		}

		if K == 0 {
			currNode := S1.head
			for currNode != 0 {
				nxt := S1.next[currNode]
				if currNode != u && !isOpen[currNode] {
					v := currNode
					inS1[v] = false
					S1.remove(v)
					dist[v][1] = dist[u][0] + 1
					parent[v][1] = State{u: u, k: 0}
					queue = append(queue, State{u: v, k: 1})
				}
				currNode = nxt
			}

			for _, v := range adj[u] {
				if inS0[v] {
					inS0[v] = false
					S0.remove(v)
					inS1[v] = true
					S1.push(v)
					dist[v][0] = dist[u][0] + 1
					parent[v][0] = State{u: u, k: 0}
					if v == n {
						printPath(parent, n)
						return
					}
					queue = append(queue, State{u: v, k: 0})
				}
			}
		} else {
			currNode := S0.head
			for currNode != 0 {
				nxt := S0.next[currNode]
				if currNode != u && !isOpen[currNode] {
					v := currNode
					inS0[v] = false
					S0.remove(v)
					inS1[v] = true
					S1.push(v)
					dist[v][0] = dist[u][1] + 1
					parent[v][0] = State{u: u, k: 1}
					if v == n {
						printPath(parent, n)
						return
					}
					queue = append(queue, State{u: v, k: 0})
				}
				currNode = nxt
			}

			for _, v := range adj[u] {
				if inS1[v] {
					inS1[v] = false
					S1.remove(v)
					dist[v][1] = dist[u][1] + 1
					parent[v][1] = State{u: u, k: 1}
					queue = append(queue, State{u: v, k: 1})
				}
			}
		}

		for _, v := range adj[u] {
			isOpen[v] = false
		}
	}

	fmt.Println("-1")
}

func printPath(parent [][2]State, n int) {
	path := []int{}
	curr := State{u: n, k: 0}
	for curr.u != 1 || curr.k != 0 {
		path = append(path, curr.u)
		curr = parent[curr.u][curr.k]
	}
	path = append(path, 1)

	fmt.Println(len(path) - 1)
	out := bufio.NewWriter(os.Stdout)
	for i := len(path) - 1; i >= 0; i-- {
		fmt.Fprintf(out, "%d ", path[i])
	}
	fmt.Fprintln(out)
	out.Flush()
}
```