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:
//package main;

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

public class Main{
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        StringBuffer outBuffer = new StringBuffer();
        
        int N = Reader.nextInt();
        int V = Reader.nextInt();
        
        Kayak[] kayaks = new Kayak[N];
        ArrayList<CapId> bigSorted = new ArrayList<CapId>();
        ArrayList<CapId> smallSorted = new ArrayList<CapId>();
        
        
        //Load arrays
        for(int n = 0; n < N; n++) {
            //Put it in the kayaks by id array
            boolean size = Reader.nextInt() == 2;
            int capacity = Reader.nextInt();
            kayaks[n] = new Kayak(capacity, size);
            //Put in the sortable Capacity+id arrays
            if(kayaks[n].big) {
                bigSorted.add(new CapId(n+1, kayaks[n].capacity));
            } else {
                smallSorted.add(new CapId(n+1, kayaks[n].capacity));
            }
        }
        
        //Sort arrays
        Collections.sort(smallSorted);
        Collections.sort(bigSorted);
        
        int v = 0;
        int cap = 0;
        int nextSmall = 0;
        int nextBig = 0;
        ArrayList<Integer> ids = new ArrayList<Integer>();
        //If odd, add small element first
        if(V % 2 == 1) {
            //Update space used
            v++;
            //If there is something to place, do so
            if(smallSorted.size() > 0) {
                nextSmall++;
                cap+= smallSorted.get(0).capacity;
                ids.add(smallSorted.get(0).id);
            }
        }
        //For remaining capacity, fill by 2s
        while(v < V) {
            //If there are both small and bigs still
            if(nextSmall < smallSorted.size() && nextBig < bigSorted.size()) {
                //compare big vs next 2 small
                CapId big = bigSorted.get(nextBig);
                CapId small = smallSorted.get(nextSmall);
                //Check for only 1 small remaining
                if(nextSmall + 1 == smallSorted.size()) {
                    if(small.capacity > big.capacity) {
                        cap+=small.capacity;
                        ids.add(small.id);
                        nextSmall++;
                    } else {
                        cap+=big.capacity;
                        ids.add(big.id);
                        nextBig++;
                    }
                } else {
                    CapId small2 = smallSorted.get(nextSmall+1);
                    if(small.capacity+small2.capacity > big.capacity) {
                        cap+=small.capacity;
                        cap+=small2.capacity;
                        ids.add(small.id);
                        ids.add(small2.id);
                        nextSmall+=2;
                    } else {
                        cap+=big.capacity;
                        ids.add(big.id);
                        nextBig++;
                    }
                }
                //Update lorry space used.
                v+= 2;
            }
            //Else add remaining of small array
            else if (nextSmall < smallSorted.size()){
                CapId small = smallSorted.get(nextSmall);
                cap+=small.capacity;
                ids.add(small.id);
                nextSmall++;
                v++;
            }
            //Else add remaining of big array
            else if (nextBig < bigSorted.size()){
                CapId big = bigSorted.get(nextBig);
                cap+=big.capacity;
                ids.add(big.id);
                nextBig++;
                v+=2;
            }
            //Else still have space but no more boats.  Break.
            else {
                break;
            }
        }
        //Output calculated capacity and ids
        outBuffer.append(cap + "\n");
        for(int i = 0; i < ids.size(); i++) {
            outBuffer.append(ids.get(i) + " ");
        }
        
        System.out.println(outBuffer);
    }
}

class Kayak {
    public int capacity;
    public boolean big;
    Kayak(int capacityIn, boolean isBig) {
        big = isBig;
        capacity = capacityIn;
    }
}

class CapId implements Comparable<CapId> {
    public int capacity;
    public int id;
    
    CapId(int idIn, int capacityIn) {
        id = idIn;
        capacity = capacityIn;
    }
    
    @Override public int compareTo(CapId aThat) {
        //Note: inverted sort ordering, goes from greatest to least
        final int BEFORE = 1;
        final int EQUAL = 0;
        final int AFTER = -1;
        
        if(this == aThat) return EQUAL;
        
        if(this.capacity < aThat.capacity) return BEFORE;
        if(this.capacity > aThat.capacity) return AFTER;
        
        if(this.id < aThat.id) return BEFORE;
        if(this.id > aThat.id) return AFTER;
        
        return EQUAL;
    }
}

// Class for buffered reading int and double values 
//Mad props go out to: http://www.cpe.ku.ac.th/~jim/java-io.html
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    //call this method to initialize reader for InputStream
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    //get next word
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}