Problem: Easy and hard versions are actually different problems, so read statements of both problems completely and carefully.

Summer vacation has started so Alice and Bob want to play and joy, but... Their mom doesn't think so. She says that they have to read some amount of books before all entertainments. Alice and Bob will read each book together to end this exercise faster.

There are n books in the family library. The i-th book is described by three integers: t_i — the amount of time Alice and Bob need to spend to read it, a_i (equals 1 if Alice likes the i-th book and 0 if not), and b_i (equals 1 if Bob likes the i-th book and 0 if not).

So they need to choose some books from the given n books in such a way that:

  * Alice likes at least k books from the chosen set and Bob likes at least k books from the chosen set; 
  * the total reading time of these books is minimized (they are children and want to play and joy as soon a possible). 



The set they choose is the same for both Alice an Bob (it's shared between them) and they read all books together, so the total reading time is the sum of t_i over all books that are in the chosen set.

Your task is to help them and find any suitable set of books or determine that it is impossible to find such a set.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5).

The next n lines contain descriptions of books, one description per line: the i-th line contains three integers t_i, a_i and b_i (1 ≤ t_i ≤ 10^4, 0 ≤ a_i, b_i ≤ 1), where:

  * t_i — the amount of time required for reading the i-th book; 
  * a_i equals 1 if Alice likes the i-th book and 0 otherwise; 
  * b_i equals 1 if Bob likes the i-th book and 0 otherwise. 

Output

If there is no solution, print only one integer -1. Otherwise print one integer T — the minimum total reading time of the suitable set of books.

Examples

Input

8 4
7 1 1
2 1 1
4 0 1
8 1 1
1 0 1
1 1 1
1 0 1
3 0 0


Output

18


Input

5 2
6 0 0
9 0 0
1 0 1
2 1 1
5 1 0


Output

8


Input

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


Output

-1

Solution (in JAVA):

Solution:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
import java.util.*;
import java.io.*;
/**
 *
 * @author billy
 */
public class ReadingBooks {

    /**
     * @param args the command line arguments
     */
    
    static class Triple implements Comparable<Triple>{
        int x;
        int y;
        int z;

        Triple (int x0, int y0, int z0){
            x=x0;
            y=y0;
            z = z0;

        }
        public int compareTo(Triple e){
            return x - e.x;
            
        }
    }
        static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    static StringTokenizer st;



    public static void main(String[] args) throws IOException {
        
        int n = readInt();
        int k = readInt();
        ArrayList<Triple> ab = new ArrayList();
        ArrayList<Integer> a = new ArrayList();
        ArrayList<Integer> b = new ArrayList();
        
        
        for (int i=0; i<n; i++){
            int t = readInt();
            int a1 = readInt();
            int b1= readInt();
            
            if (a1 ==1 && b1==1){
                ab.add(new Triple(t,a1,b1));
            }
            else if (a1==1 && b1==0){
                a.add(t);
            }
            else if (a1==0 && b1==1){
                b.add(t);
            }
            else{
                continue;
            }
        }
        Collections.sort(a);
        Collections.sort(b);
        
        for (int i =0; i<Math.min(a.size(), b.size()); i++){
            int t1 = a.get(i);
            int t2 = b.get(i);
            ab.add(new Triple(t1+t2,1,1));
        }
        Collections.sort(ab);
        long ans = 0;
        int ak = 0;
        int bk = 0;
       
        for (int i =0; i<ab.size();i++){
            ans+=ab.get(i).x;
            ak++;
            bk++;
            if (ak>=k){
                break;
            }
        }
        if (ak<k){
            System.out.println(-1);
        }
        else{
            System.out.println(ans);
        }
        
        
        
        
        /*
        three lists types to consider
        AB: add to this list
        A: sort by times
        B: sort by times
        pair up A and B to make AB, add to AB list, and sort again
        
        
        */
        
    }





    static String read () throws IOException {
        while (st == null || !st.hasMoreTokens())
           st = new StringTokenizer(br.readLine().trim());
        return st.nextToken();
    }
    //© Maillew DMOJ
    static long readLong () throws IOException {
        return Long.parseLong(read());
    }
    static int readInt () throws IOException {
        return Integer.parseInt(read());
    }
    static double readDouble () throws IOException {
        return Double.parseDouble(read());
    }
    static char readChar () throws IOException {
        return read().charAt(0);
    }
    static String readLine () throws IOException {
        return br.readLine().trim();
    }
   
    
}