Problem: There are n students at Berland State University. Every student has two skills, each measured as a number: ai — the programming skill and bi — the sports skill.

It is announced that an Olympiad in programming and sports will be held soon. That's why Berland State University should choose two teams: one to take part in the programming track and one to take part in the sports track.

There should be exactly p students in the programming team and exactly s students in the sports team. A student can't be a member of both teams.

The university management considers that the strength of the university on the Olympiad is equal to the sum of two values: the programming team strength and the sports team strength. The strength of a team is the sum of skills of its members in the corresponding area, so the strength of the programming team is the sum of all ai and the strength of the sports team is the sum of all bi over corresponding team members.

Help Berland State University to compose two teams to maximize the total strength of the university on the Olympiad.

Input

The first line contains three positive integer numbers n, p and s (2 ≤ n ≤ 3000, p + s ≤ n) — the number of students, the size of the programming team and the size of the sports team.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 3000), where ai is the programming skill of the i-th student.

The third line contains n positive integers b1, b2, ..., bn (1 ≤ bi ≤ 3000), where bi is the sports skill of the i-th student.

Output

In the first line, print the the maximum strength of the university on the Olympiad. In the second line, print p numbers — the members of the programming team. In the third line, print s numbers — the members of the sports team.

The students are numbered from 1 to n as they are given in the input. All numbers printed in the second and in the third lines should be distinct and can be printed in arbitrary order.

If there are multiple solutions, print any of them.

Examples

Input

5 2 2
1 3 4 5 2
5 3 2 1 4


Output

18
3 4 
1 5 


Input

4 2 2
10 8 8 3
10 7 9 4


Output

31
1 2 
3 4 


Input

5 3 1
5 2 5 1 7
6 3 1 6 3


Output

23
1 3 5 
4 

Solution (in JAVA):

Solution:
import sun.reflect.generics.tree.Tree;

import java.io.*;
import java.util.*;

public class I_special4
{
    private static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
    private static StringTokenizer stringTokenizer = null;
    private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    private static String next() throws IOException
    {
        while ((stringTokenizer == null) || (!stringTokenizer.hasMoreTokens()))
        {
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());
        }
        return stringTokenizer.nextToken();
    }

    public static int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }

    public static double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }

    public static long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }

    public static String nextLine() throws IOException
    {
        return bufferedReader.readLine();
    }

    public static void close()
    {
        out.close();
    }

    public static final long[] POWER2 = generatePOWER2();

    public static long[] generatePOWER2()
    {
        long[] result = new long[63];
        for (int x = 0; x < result.length; x++)
        {
            result[x] = 1L << x;
        }
        return result;
    }

    static class Tuple2<Type0, Type1>
    {
        public final Type0 v0;
        public final Type1 v1;

        public Tuple2(Type0 v0, Type1 v1)
        {
            this.v0 = v0;
            this.v1 = v1;
        }
    }

    static class Tuple2Comparable<Type0 extends Comparable<? super Type0>, Type1 extends Comparable<? super Type1>> extends Tuple2<Type0, Type1> implements Comparable<Tuple2Comparable<Type0, Type1>>
    {
        public Tuple2Comparable(Type0 v0, Type1 v1)
        {
            super(v0, v1);
        }

        @Override
        public int compareTo(Tuple2Comparable<Type0, Type1> that)
        {
            int result = this.v0.compareTo(that.v0);
            if (result == 0)
            {
                result = this.v1.compareTo(that.v1);
            }
            return result;
        }
    }

    static class LinkedList<Type>
    {
        public final Type element;
        public final LinkedList<Type> next;

        public LinkedList(Type element, LinkedList<Type> next)
        {
            this.element = element;
            this.next = next;
        }

        public void toCollection(Collection<Type> collection)
        {
            if (this.next != null)
            {
                this.next.toCollection(collection);
            }
            collection.add(this.element);
        }
    }

    public static long faculty(int n)
    {
        long result = 1;
        for (int index = 2; index <= n; index++)
        {
            result *= index;
        }
        return result;
    }

    public static <T> List<T> permutation(long p, List<T> x)
    {
        List<T> copy = new ArrayList<>();
        for (int index = 0; index < x.size(); index++)
        {
            copy.add(x.get(index));
        }
        List<T> result = new ArrayList<>();
        for (int indexTo = 0; indexTo < x.size(); indexTo++)
        {
            int indexFrom = (int) p % copy.size();
            p = p / copy.size();
            result.add(copy.remove(indexFrom));
        }
        return result;
    }

    public static <T> void print(T[] elements)
    {
        for (int index = 0; index < elements.length; index++)
        {
            out.print((index > 0 ? " " : "") + elements[index].toString());
        }
        out.println();
    }

    public static void main(String[] args)
    {
        try
        {
            solve();
        } catch (IOException exception)
        {
            exception.printStackTrace();
        }
        close();
    }

    static class Student implements Comparable<Student>
    {
        public final int index;
        public final int skillProgramming;
        public final int skillSporting;

        public Student(int index, int skillProgramming, int skillSport)
        {
            this.index = index;
            this.skillProgramming = skillProgramming;
            this.skillSporting = skillSport;
        }

        public String toString()
        {
            return "" + (index + 1);
        }

        public int betterAsSporter()
        {
            return this.skillSporting - this.skillProgramming;
        }

        @Override
        public int compareTo(Student that)
        {
            return Integer.compare(this.index, that.index);
        }
    }

    public static int scoreMaximum(int p, Student[] team)
    {
        Arrays.sort(team, (x, y) -> Integer.compare(x.betterAsSporter(), y.betterAsSporter()));
        int result = 0;
        for (int index = 0; index < p; index++)
        {
            result += team[index].skillProgramming;
        }
        for (int index = p; index < team.length; index++)
        {
            result += team[index].skillSporting;
        }
        return result;
    }


    public static void solve(int p, int s, Student[] team, Student student)
    {
        int score = scoreMaximum(p, team);
        int scoreMaximum = score;
        Integer indexMaximum = null;
        for (int index = 0; index < team.length; index++)
        {
            int scoreNew = score;
            if (p == 0)
            {
                scoreNew -= team[index].skillSporting;
                scoreNew += student.skillSporting;
            }
            else
            {
                if (s == 0)
                {
                    scoreNew -= team[index].skillProgramming;
                    scoreNew += student.skillProgramming;
                }
                else
                {
                    if (index < p)
                    {
                        scoreNew -= team[index].skillProgramming;
                        Student firstSporter = team[p];
                        if (student.betterAsSporter() < firstSporter.betterAsSporter())
                        {
                            scoreNew += student.skillProgramming;
                        }
                        else
                        {
                            scoreNew += student.skillSporting;
                            scoreNew -= firstSporter.skillSporting;
                            scoreNew += firstSporter.skillProgramming;
                        }
                    }
                    else
                    {
                        scoreNew -= team[index].skillSporting;
                        Student lastProgrammer = team[p - 1];
                        if (lastProgrammer.betterAsSporter() < student.betterAsSporter())
                        {
                            scoreNew += student.skillSporting;
                        }
                        else
                        {
                            scoreNew += student.skillProgramming;
                            scoreNew -= lastProgrammer.skillProgramming;
                            scoreNew += lastProgrammer.skillSporting;
                        }
                    }
                }
            }
            if (scoreMaximum < scoreNew)
            {
                scoreMaximum = scoreNew;
                indexMaximum = index;
            }
        }
        if (indexMaximum != null)
        {
            team[indexMaximum] = student;
        }
    }


    public static Student[] solve(int p, int s, Student[] students)
    {
        Student[] result = Arrays.copyOf(students, p + s);
        for (int index = p + s; index < students.length; index++)
        {
            solve(p, s, result, students[index]);
        }
        return result;
    }

    public static void solve() throws IOException
    {
        int n = nextInt();
        int p = nextInt();
        int s = nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int index = 0; index < n; index++)
        {
            a[index] = nextInt();
        }
        for (int index = 0; index < n; index++)
        {
            b[index] = nextInt();
        }
        Student[] students = new Student[n];
        for (int index = 0; index < n; index++)
        {
            students[index] = new Student(index, a[index], b[index]);
        }
        Student[] team = solve(p, s, students);
        int scoreMaximum = scoreMaximum(p, team);
        out.println(scoreMaximum);
        print(Arrays.copyOfRange(team, 0, p));
        print(Arrays.copyOfRange(team, p, p + s));
    }
}