Problem: A group of tourists is going to kayak and catamaran tour. A rented lorry has arrived to the boat depot to take kayaks and catamarans to the point of departure. It's known that all kayaks are of the same size (and each of them occupies the space of 1 cubic metre), and all catamarans are of the same size, but two times bigger than kayaks (and occupy the space of 2 cubic metres).

Each waterborne vehicle has a particular carrying capacity, and it should be noted that waterborne vehicles that look the same can have different carrying capacities. Knowing the truck body volume and the list of waterborne vehicles in the boat depot (for each one its type and carrying capacity are known), find out such set of vehicles that can be taken in the lorry, and that has the maximum total carrying capacity. The truck body volume of the lorry can be used effectively, that is to say you can always put into the lorry a waterborne vehicle that occupies the space not exceeding the free space left in the truck body.

Input

The first line contains a pair of integer numbers n and v (1 ≤ n ≤ 105; 1 ≤ v ≤ 109), where n is the number of waterborne vehicles in the boat depot, and v is the truck body volume of the lorry in cubic metres. The following n lines contain the information about the waterborne vehicles, that is a pair of numbers ti, pi (1 ≤ ti ≤ 2; 1 ≤ pi ≤ 104), where ti is the vehicle type (1 – a kayak, 2 – a catamaran), and pi is its carrying capacity. The waterborne vehicles are enumerated in order of their appearance in the input file.

Output

In the first line print the maximum possible carrying capacity of the set. In the second line print a string consisting of the numbers of the vehicles that make the optimal set. If the answer is not unique, print any of them.

Examples

Input

3 2
1 2
2 7
1 3


Output

7
2

Solution (in JAVA):

Solution:
/**
 * ******* Created on 18/9/19 1:58 AM*******
 */

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

public class BCon3 {
    public static void main(String[] args) throws IOException {
        final class Pair{
            long a;
            int b;
            public Pair(long x, int y){
                 a=x;
                 b=y;
            }
        }
        try (Input input = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            long n = input.nextLong();
            long v = input.nextLong();
            ArrayList<Pair>kayak = new ArrayList<>();
            ArrayList<Pair>cata = new ArrayList<>();
            for(int i=0;i<n;i++){
                int t = input.nextInt();
                long p = input.nextLong();
                if(t==1)kayak.add(new Pair(p,i));
                else cata.add(new Pair(p,i));
            }
            Collections.sort(kayak, new Comparator<Pair>() {
                @Override
                public int compare(Pair o1, Pair o2) {
                    return (int) (o1.a-o2.a);
                }
            });
            Collections.sort(cata, new Comparator<Pair>() {
                @Override
                public int compare(Pair o1, Pair o2) {
                    return (int) (o1.a -o2.a);
                }
            });
            int ind1 = kayak.size()-1;
            int ind2 = cata.size()-1;
            ArrayList<Integer> list = new ArrayList<>();
            long ans =0;
            while(v >1 && (ind1>=0 || ind2>=0)){
                long val1 =ind1>=0 ? (kayak.get(ind1).a)*2:0;
                long val2 = ind2 >=0 ?cata.get(ind2).a:0;

                if(val1 > val2 && ind1!=0 || (ind2 <0)){
                    ans+= kayak.get(ind1).a;
                    list.add(kayak.get(ind1).b);
                    ind1--;v--;
                }else {
                    ans += cata.get(ind2).a;
                    list.add(cata.get(ind2).b);
                    ind2--;
                    v-=2;
                }

             }
            if(v== 1 && ind1 >=0){
                ans += kayak.get(ind1).a;
                list.add(kayak.get(ind1).b);
            }
            System.out.println(ans);
            for(int i=0;i<list.size();i++) System.out.print( (list.get(i)+1) + " ");
            System.out.println();
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

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

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

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

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}