Frog Gorf is traveling through Swamp kingdom. Unfortunately, after a poor jump, he fell into a well of n meters depth. Now Gorf is on the bottom of the well and has a long way up.

The surface of the well's walls vary in quality: somewhere they are slippery, but somewhere have convenient ledges. In other words, if Gorf is on x meters below ground level, then in one jump he can go up on any integer distance from 0 to a_x meters inclusive. (Note that Gorf can't jump down, only up).

Unfortunately, Gorf has to take a break after each jump (including jump on 0 meters). And after jumping up to position x meters below ground level, he'll slip exactly b_x meters down while resting.

Calculate the minimum number of jumps Gorf needs to reach ground level.

Input

The first line contains a single integer n (1 ≤ n ≤ 300 000) — the depth of the well.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i), where a_i is the maximum height Gorf can jump from i meters below ground level.

The third line contains n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ n - i), where b_i is the distance Gorf will slip down if he takes a break on i meters below ground level.

Output

If Gorf can't reach ground level, print -1. Otherwise, firstly print integer k — the minimum possible number of jumps.

Then print the sequence d_1,\,d_2, …,\,d_k where d_j is the depth Gorf'll reach after the j-th jump, but before he'll slip down during the break. Ground level is equal to 0.

If there are multiple answers, print any of them.

Examples

Input


3
0 2 2
1 1 0


Output


2
1 0 


Input


2
1 1
1 0


Output


-1


Input


10
0 1 2 3 5 5 6 7 8 5
9 8 7 1 5 4 3 2 0 0


Output


3
9 4 0 

Note

In the first example, Gorf is on the bottom of the well and jump to the height 1 meter below ground level. After that he slip down by meter and stays on height 2 meters below ground level. Now, from here, he can reach ground level in one jump.

In the second example, Gorf can jump to one meter below ground level, but will slip down back to the bottom of the well. That's why he can't reach ground level.

In the third example, Gorf can reach ground level only from the height 5 meters below the ground level. And Gorf can reach this height using a series of jumps 10 ⇒ 9 \dashrightarrow 9 ⇒ 4 \dashrightarrow 5 where ⇒ is the jump and \dashrightarrow is slipping during breaks.
19
1 1 3 4 5 3 5 7 0 6 5 3 10 3 13 9 1 4 17
3 0 6 3 8 6 8 7 8 6 0 0 5 0 0 1 1 1 0
 10
1 0 2 2 5 0 0 0 2 7
4 3 1 0 4 3 3 2 1 0
 5
0 0 1 4 2
0 2 0 1 0
 10
1 1 1 0 3 0 6 2 4 5
7 6 2 3 5 1 2 0 1 0
 1
1
0
 12
1 0 0 1 2 5 5 1 9 6 2 9
8 8 8 1 1 4 4 0 3 1 1 0

3
2 1 0  3
3 2 0  3
3 2 0  -1
 1
0  3
5 1 0 

import java.util.*;

import javax.swing.text.Segment;

import java.io.*;
import java.math.*;
import java.sql.Array;



public class Main {
	  static class Scanner{
		  
			BufferedReader br;
			StringTokenizer st;
			public Scanner() {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
			String next() 
		    { 
		        while (st == null || !st.hasMoreElements()) 
		        { 
		            try
		            { 
		                st = new StringTokenizer(br.readLine()); 
		            } 
		            catch (IOException  e) 
		            { 
		                e.printStackTrace(); 
		            } 
		        } 
		        return st.nextToken(); 
		    } 

		    int nextInt() 
		    { 
		        return Integer.parseInt(next()); 
		    } 

		    long nextLong() 
		    { 
		        return Long.parseLong(next()); 
		    } 

		    double nextDouble() 
		    { 
		        return Double.parseDouble(next()); 
		    } 

		    String nextLine() 
		    { 
		        String str = ""; 
		        try
		        { 
		            str = br.readLine(); 
		        } 
		        catch (IOException e) 
		        { 
		            e.printStackTrace(); 
		        } 
		        return str; 
		    } 
		}
	 
	  static long mod = (long)(1e9 + 7);
	 
	static void sort(long[] arr ) {
		 ArrayList<Long> al = new ArrayList<>();
		 for(long e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(int[] arr ) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for(int e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(char[] arr) {
		ArrayList<Character> al = new ArrayList<Character>();
		for(char cc:arr) al.add(cc);
		Collections.sort(al);
		for(int i = 0 ;i<arr.length ;i++) arr[i] = al.get(i);
	}
	static void rvrs(int[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			int temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}
	static void rvrs(long[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			long temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}

	static long mod_mul(long a , long b ,long mod) {
		return ((a%mod)*(b%mod))%mod;
	}
	 static long gcd(long a, long b)
	  {      
	     if (b == 0)
	        return a;
	     return gcd(b, a % b); 
	  }
	 static boolean[] prime(int num) {
			boolean[] bool = new boolean[num];
		     
		      for (int i = 0; i< bool.length; i++) {
		         bool[i] = true;
		      }
		      for (int i = 2; i< Math.sqrt(num); i++) {
		         if(bool[i] == true) {
		            for(int j = (i*i); j<num; j = j+i) {
		               bool[j] = false;
		            }
		         }
		      }
		      if(num >= 0) {
		    	  bool[0] = false;
		    	  bool[1] = false;
		      }
		      
		      return bool;
		}

	 static long modInverse(long a, long m)
	    {
	        long g = gcd(a, m);
	       
	          return   power(a, m - 2, m);
	        
	    }
	   
	 static long power(long x, long y, long m){
	        if (y == 0) return 1; long p = power(x, y / 2, m) % m; p = (int)((p * (long)p) % m);
	        if (y % 2 == 0) return p; else return (int)((x * (long)p) % m); }
	   
     static class Combinations{
	    	 private long[] z;
	    	 private long[] z1;
	    	 private long[] z2;
	    	  public Combinations(long N , long mod) {
				z = new long[(int)N+1];
				z1 = new long[(int)N+1];
				z[0] = 1;
				for(int i =1 ; i<=N ; i++) z[i] = (z[i-1]*i)%mod;
			     z2 = new long[(int)N+1];
				z2[0] = z2[1] = 1;
			    for (int i = 2; i <= N; i++)
			        z2[i] = z2[(int)(mod % i)] * (mod - mod / i) % mod;
			    
			    
			    z1[0] = z1[1] = 1;
			    
			    for (int i = 2; i <= N; i++)
			        z1[i] = (z2[i] * z1[i - 1]) % mod;
			}
	    	  long fac(long n) {
	    		  return z[(int)n];
	    	  }
	    	  long invrsNum(long n) {
	    		  return z2[(int)n];
	    	  }
	    	  long invrsFac(long n) {
	    		  return invrsFac((int)n);
	    	  }
	    	  long ncr(long N, long R, long mod)
	    	  {		if(R<0 || R>N ) return 0;
	    		    long ans = ((z[(int)N] * z1[(int)R])
	    		              % mod * z1[(int)(N - R)])
	    		             % mod;
	    		    return ans;
	    		}
	      }
	      static class DisjointUnionSets {
			    int[] rank, parent;
			    int n;
			  
			    public DisjointUnionSets(int n)
			    {
			        rank = new int[n];
			        parent = new int[n];
			        this.n = n;
			        makeSet();
			    }
			  
			    void makeSet()
			    {
			        for (int i = 0; i < n; i++) {
			          
			            parent[i] = i;
			        }
			    }
			  
			    int find(int x)
			    {
			        if (parent[x] != x) {
			        
			            parent[x] = find(parent[x]);
			  
			        }
			  
			        return parent[x];
			    }
			  
			    void union(int x, int y)
			    {
			        int xRoot = find(x), yRoot = find(y);
			  
			        if (xRoot == yRoot)
			            return;
			  
			        if (rank[xRoot] < rank[yRoot])
			  
			            parent[xRoot] = yRoot;
			  
			        else if (rank[yRoot] < rank[xRoot])
			  
			            parent[yRoot] = xRoot;
			  
			        else
			        {
			            parent[yRoot] = xRoot;
			  
			            rank[xRoot] = rank[xRoot] + 1;
			        }
			    }
			}
	      static int max(int a , int b) {
	    	  if(b>a) return b;
	    	  return a;  
	      }
	      static long max(long a , long b) {
	    	  if(b>a) return b;
	    	  return a;  
	      }
	      static int min(int a , int b) {
	    	  if(b<a) return b;
	    	  return a;
	      }
	      static long min(long a , long b) {
	    	  if(b<a) return b;
	    	  return a;
	      }
	      static int[] KMP(String str) {
	    	  int n = str.length();
	    	  int[] kmp = new int[n];
	    	  for(int i = 1 ; i<n ; i++) {
	    		  int j = kmp[i-1];
	    		  while(j>0 && str.charAt(i) != str.charAt(j)) {
	    			  j = kmp[j-1];
	    		  }
	    		  if(str.charAt(i) == str.charAt(j)) j++;
	    		  kmp[i] = j;
	    	  }
	    	  
	    	  return kmp;
	      }
	      
	      
/************************************************ Query **************************************************************************************/	  
	 
/***************************************** 		Sparse Table	********************************************************/
	      static class SparseTable{
	    		
	    		private long[][] st;
	    		
	    		SparseTable(long[] arr){
	    			int n = arr.length;
	    			st = new long[n][25];
	    			log = new int[n+2];
	    			build_log(n+1);
	    			build(arr);
	    		}
	    		
	    		private void build(long[] arr) {
	    			int n = arr.length;
	    			
	    			for(int i = n-1 ; i>=0 ; i--) {
	    				for(int j = 0 ; j<25 ; j++) {
	    					int r = i + (1<<j)-1;
	    					if(r>=n) break;
	    					if(j == 0 ) st[i][j] = arr[i];
	    					else st[i][j] = Math.max(st[i][j-1] , st[ i + ( 1 << (j-1) ) ][ j-1 ] );
	    				}
	    			}
	    		}
	    		public long gcd(long a  ,long b) {
	    			if(a == 0) return b;
	    			return gcd(b%a , a);
	    		}
	    		public long query(int l ,int r) {
	    			int w = r-l+1;
	    			int power = log[w];
	    			return Math.max(st[l][power],st[r - (1<<power) + 1][power]);
	    		}
	    		private int[] log;
	    		void build_log(int n) {
	    			log[1] = 0;
	    			for(int i = 2 ; i<=n ; i++) {
	    				log[i] = 1 + log[i/2];
	    			}
	    		}
	    	}
	      
	      
/********************************************************	Segement Tree	*****************************************************/
/**
	 	 static class SegmentTree{
			 long[] tree;
			 long[] arr;
			 int n;
			 SegmentTree(long[] arr){
				 this.n = arr.length;
				 tree = new long[4*n+1];
				 this.arr = arr;
				 buildTree(0, n-1, 1);
			 }
			 
			 
			  void buildTree(int s ,int e  ,int index ) {
					if(s == e) {
						tree[index] = arr[s];
						return;
					}
				
					int mid = (s+e)/2;
					
					buildTree( s,  mid, 2*index);
					buildTree( mid+1, e, 2*index+1);
					
					tree[index] = Math.min(tree[2*index] , tree[2*index+1]);
				}
			  
			 long query(int si ,int ei) {
				 return query(0 ,n-1 , si ,ei , 1   );
			 }
			 private long query( int ss ,int se ,int qs , int qe,int index) {
					
					if(ss>=qs && se<=qe) return tree[index];
					
					if(qe<ss || se<qs) return (long)(1e17);
					
					int mid = (ss + se)/2;
					long left = query( ss , mid , qs ,qe , 2*index);
					long right= query(mid + 1 , se , qs ,qe , 2*index+1);
					return Math.min(left, right);
				}
			 public void update(int index , int val) {
				 arr[index] = val;
				 for(long e:arr) System.out.print(e+" ");
				 update(index , 0 , n-1 , 1);
			 }
			 private void update(int id ,int si , int ei , int index) {
				 if(id < si || id>ei) return;
				 if(si == ei ) { 
					 tree[index] = arr[id];
					 return;
				 }
				 if(si > ei) return;
				 int mid = (ei + si)/2;
					
					update( id,  si, mid , 2*index);
					update( id , mid+1, ei , 2*index+1);
					
					tree[index] = Math.min(tree[2*index] ,tree[2*index+1]);
			 }
			  
		 }
		 */

/* ***************************************************************************************************************************************************/	 
	 
	      static Scanner sc = new Scanner();
	 static StringBuilder sb = new StringBuilder();
	 public static void main(String args[]) throws IOException {
	
		 int tc = 1;
//		  tc = sc.nextInt();
		 for(int i = 1 ; i<=tc ; i++) {

//			 sb.append("Case #" + i + ": "  );	// During KickStart && HackerCup
			 TEST_CASE();
			 
		 }
		 System.out.println(sb);
	 }
	 static void TEST_CASE() {
		int n = sc.nextInt();
		int[] a = new int[n+1] , b = new int[n+1];
		for(int i = 1 ; i<=n ; i++)
			a[i] = sc.nextInt();
		
		for(int i = 1 ; i<=n ; i++)
			b[i] = sc.nextInt();
		
		bfs(a, b);
		
	 }
	static void bfs(int[] a , int[] b) {
		int n = a.length-1;
		boolean[] visit = new boolean[n+1];
		boolean result = false;
		TreeSet<Integer> tree = new TreeSet<Integer>();
		for(int i = 0 ; i<=n ; i++) tree.add(i);
		LinkedList<Pair> ll = new LinkedList<>();
		ll.add(new Pair(n , 0,-1 ));
		int[] graph = new int[n+1];
		int ans = -1;
		while(!ll.isEmpty()) {
			Pair pp = ll.removeFirst();
//			System.out.println(pp);
			if(visit[pp.x]) continue;
			graph[pp.x] = pp.prv;
			if(pp.x == 0) {
				result = true;
				ans = pp.y;
				break;
			}
			visit[pp.x] = true;
			int shift = pp.x + b[pp.x];
			tree.remove(shift);
			int s = Math.max(0, shift - a[shift]) , e = Math.max(0 ,shift - 1  );
			while(tree.ceiling(s) != null && tree.ceiling(s) <= e) {
				int pi = tree.ceiling(s);
				tree.remove(pi);
				ll.addLast(new Pair(pi , pp.y+1 , pp.x));
			}
		}
		if(!result) {
			sb.append("-1\n");
			return;
		}else {
			LinkedList<Integer> l = new LinkedList<>();
			l.add(0);
			while(graph[l.peek()]!=-1) {
				l.addFirst(graph[l.peekFirst()]);
			}
			l.removeFirst();
			sb.append(ans+"\n");
			while(!l.isEmpty()) {
				sb.append(l.removeFirst()+" ");
			}
		}
	}
	static class Pair{
		int x;
		int y;
		int prv;
		Pair(int x, int y , int prv){
			this.x = x;
			this.y = y;
			this.prv = prv;
		}
		public String toString() {
			return "{"+this.x+","+this.y+","+this.prv+   "}";
		}
	}
}

	 

/*******************************************************************************************************************************************************/

/**


 */

 

