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 java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class I_NEERC_2016 {

	public static long MOD = 1000000007;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int p = in.nextInt();
		int s = in.nextInt();
		int[][] data = new int[n][3];
		for (int i = 1; i < 3; i++) {

			for (int j = 0; j < n; j++) {
				data[j][0] = j;
				data[j][i] = in.nextInt();
			}
		}
		Arrays.sort(data, new Comparator<int[]>() {

			@Override
			public int compare(int[] o1, int[] o2) {
				return Integer.compare(o2[1], o1[1]);
			}
		});
		int[] check = new int[n];
		Arrays.fill(check, -1);
		int total = 0;
		for (int i = 0; i < p; i++) {
			check[data[i][0]] = 0;
			total += data[i][1];
		}
		// System.out.println(Arrays.toString(check) + " " + p);
		Arrays.sort(data, new Comparator<int[]>() {

			@Override
			public int compare(int[] o1, int[] o2) {
				return Integer.compare(o2[2], o1[2]);
			}
		});
		int count = 0;
		for (int i = 0; i < n && count < s; i++) {
			if (check[data[i][0]] == -1) {
				check[data[i][0]] = 1;
				total += data[i][2];
				count++;
			}
		}
		boolean change = true;
		while (change) {
			while (change) {
				change = false;
				for (int i = 0; i < n && !change; i++) {
					if (check[data[i][0]] == 0) {
						for (int j = 0; j < n; j++) {
							if (check[data[j][0]] == 1) {
								if (data[i][2] + data[j][1] > data[i][1]
										+ data[j][2]) {
									check[data[i][0]] = 1;
									check[data[j][0]] = 0;
									total += (data[i][2] + data[j][1]
											- data[i][1] - data[j][2]);
									change = true;
									break;
								}
							}
						}
					}
				}
			}
			int max = -1;
			int min = -1;
			for (int i = 0; i < n; i++) {
				if (check[data[i][0]] == -1) {
					if (max == -1 || data[i][1] > data[max][1]) {
						max = i;
					}
				} else if (check[data[i][0]] == 0) {
					if (min == -1 || data[i][1] < data[min][1]) {
						min = i;
					}
				}
			}
			if (max != -1 && min != -1 && data[max][1] > data[min][1]) {
				check[data[max][0]] = 0;
				check[data[min][0]] = -1;
				total += data[max][1] - data[min][1];
				change = true;
			}

			max = -1;
			int a = -1, b = -1;
			for (int i = 0; i < n; i++) {
				if (check[data[i][0]] == 0) {
					if (a == -1
							|| data[i][2] - data[i][1] > data[a][2]
									- data[a][1]) {
						a = i;
					}

				} else if (check[data[i][0]] == 1) {
					if (b == -1 || data[i][2] < data[b][2]) {
						b = i;
					}
				} else {
					if (max == -1 || data[i][1] > data[max][1]) {
						max = i;
					}
				}
			}
			if (a != -1 && b != -1 && max != -1
					&& data[a][2] + data[max][1] > data[a][1] + data[b][2]) {
				check[data[a][0]] = 1;
				check[data[max][0]] = 0;
				check[data[b][0]] = -1;
				total += (data[a][2] + data[max][1] - data[a][1] - data[b][2]);
				change = true;

			}

			max = -1;
			min = -1;
			for (int i = 0; i < n; i++) {
				if (check[data[i][0]] == -1) {
					if (max == -1 || data[i][2] > data[max][2]) {
						max = i;
					}
				} else if (check[data[i][0]] == 1) {
					if (min == -1 || data[i][2] < data[min][2]) {
						min = i;
					}
				}
			}
			if (max != -1 && min != -1 && data[max][2] > data[min][2]) {
				check[data[max][0]] = 1;
				check[data[min][0]] = -1;
				total += data[max][2] - data[min][2];
				change = true;
			}
			max = -1;

			a = -1;
			b = -1;
			for (int i = 0; i < n; i++) {
				if (check[data[i][0]] == 0) {
					if (a == -1 || data[i][1] < data[a][1]) {
						a = i;
					}

				} else if (check[data[i][0]] == 1) {
					if (b == -1
							|| data[i][1] - data[i][2] > data[b][1]
									- data[b][2]) {
						b = i;
					}
				} else {
					if (max == -1 || data[i][2] > data[max][2]) {
						max = i;
					}
				}
			}
			if (a != -1 && b != -1 && max != -1
					&& data[b][1] + data[max][2] > data[b][2] + data[a][1]) {
				check[data[b][0]] = 0;
				check[data[max][0]] = 1;
				check[data[a][0]] = -1;
				total += (data[b][1] + data[max][2] - data[b][2] - data[a][1]);
				change = true;

			}

		}
		out.println(total);
		// System.out.println(Arrays.toString(check));
		for (int i = 0; i < n; i++) {
			if (check[i] == 0) {
				out.print((i + 1) + " ");
			}
		}
		out.println();
		for (int i = 0; i < n; i++) {
			if (check[i] == 1) {
				out.print((i + 1) + " ");
			}
		}
		out.println();
		out.close();
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return Integer.compare(x, o.x);
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}