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:
// package com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class DR5 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args)throws Exception{
        FastReader scan=new FastReader(System.in);
        int t=1;
//        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            int k=scan.nextInt();
            book[] arr=new book[n];
            int al=0;
            int bl=0;
            for(int i=0;i<n;i++){
                int ti=scan.nextInt();
                int a=scan.nextInt();
                int b=scan.nextInt();
                if(a==1){
                    al+=1;
                }if(b==1){
                    bl+=1;
                }
                arr[i]=new book(ti,a,b);
            }
            if(al<k||bl<k){
                out.println(-1);
            }else{
                Arrays.sort(arr);
                ArrayList<Integer> oal=new ArrayList<>();
                ArrayList<Integer> obl=new ArrayList<>();
                ArrayList<Integer> abl=new ArrayList<>();
                for(int i=0;i<n;i++){
                    book cur=arr[i];
                    if(cur.a==1&&cur.b==1){
                        abl.add(i);
                    }else{
                        if(cur.a==1){
                            oal.add(i);
                        }if(cur.b==1){
                            obl.add(i);
                        }
                    }
                }
                int ap=0;
                int bp=0;
                int cp=0;
                int an=k-Math.min(k,oal.size());
                int bn=k-Math.min(k,obl.size());
                cp=Math.max(an,bn);
                long ans=0;
                for(int i=0;i<cp;i++){
                    ans+=arr[abl.get(i)].t;
                    k--;
                }
                while(k>0){
                    long at=arr[oal.get(ap)].t;
                    long bt=arr[obl.get(bp)].t;
                    long ct=Integer.MAX_VALUE;
                    if(cp<abl.size()){
                        ct=arr[abl.get(cp)].t;
                    }
                    if(at+bt<=ct){
                        ans+=at+bt;
                        ap++;
                        bp++;
                    }else{
                        ans+=ct;
                        cp++;
                    }
                    k--;
                }
                out.println(ans);
            }
        }
        out.flush();
        out.close();
    }
    static class book implements Comparable<book>{
        int t;
        int a;
        int b;
        book(int t,int a,int b){
            this.t=t;
            this.a=a;
            this.b=b;
        }

        @Override
        public int compareTo(book o) {
            return this.t-o.t;
        }
    }
    static class FastReader {
        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;

        FastReader(InputStream is) {
            in = is;
        }

        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }

        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }

        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
}