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:

import java.util.*;
import java.io.*;
 
public class Mamo {
    static long mod=998244353;
    static Reader in=new Reader();
    static List<Integer >G[];
    static boolean B=true;
    static StringBuilder Sl=new StringBuilder();
    static int DP[][];
    public static void main(String [] args) {
    	//Dir by MohammedElkady
    int t=1;
    	while(t-->0) {
    		int n=in.nextInt(),k=in.nextInt();
    		node[]node=new node[n];
    		for(int i=0;i<n;i++) {
    			int tt=in.nextInt(),a=in.nextInt(),b=in.nextInt();
    			node[i]=new node(tt,a,b);
    		}
    		long ans=0L;
    		Arrays.parallelSort(node);
    		ArrayList<Integer>bob=new ArrayList(),eles=new ArrayList(),all=new ArrayList();
    		for(int i=0;i<n;i++) {
    			if(node[i].a==1&&node[i].b==1) {all.add(node[i].f);}
    			else if(node[i].a==1&&eles.size()<k) {eles.add(node[i].f);}
    			else if(node[i].b==1&&bob.size()<k) {bob.add(node[i].f);}
    			
    		}
    		if(bob.size()+(2*all.size())+eles.size()<k) {out.append("-1"+"\n");}
    		else {
    			int i=0,u=0,v=0;
    			while(k>0&&i<all.size()&&u<eles.size()&&bob.size()>v) {
    				k--;
    				if(all.get(i)>eles.get(u)+bob.get(v)) {
    					ans+=(eles.get(u)+bob.get(v));
    					u++;v++;
    				}
    				else {ans+=(all.get(i));i++;}	
    			}
    			while(all.size()>i&&k>0) {ans+=(all.get(i));i++;k--;}
    			while(k>0&&eles.size()>u&&bob.size()>v) {k--;
    			ans+=(eles.get(u)+bob.get(v));
				u++;v++;
    			}
    			if(k>0)
    				out.append(-1+"\n");
    			else 
    			out.append(ans+"\n");
    		}
    	}
    out.close();}
//    static int[]fromlist(ArrayList<Integer>l){
//    	int a[]=new int[l.size()];
//    	for(int i=0;i<l.size();i++)a[i]=l.get(i);
//    }
    
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long gcd(long g,long x){if(x<1)return g;else return gcd(x,g%x);}
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int nextInt(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = nextInt();}return ret;}
    }
}
class node implements Comparable<node>{
int f, a,b;
node(int tt,int ll,int vv){
f=tt;a=ll;b=vv;
}
    @Override
    public int compareTo(node o) {
    return f-o.f;    
    }
}
class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
}
 
class Sorting{
 
 public static node[] bucketSort(node[] array, int bucketCount) {
 
 if (bucketCount <= 0) throw new IllegalArgumentException("Invalid bucket count");
 
 if (array.length <= 1) return array; //trivially sorted
 
 
 
 int high = array[0].f;
 
 int low = array[0].f;
 
 for (int i = 1; i < array.length; i++) { //find the range of input elements
 
 if (array[i].f > high) high = array[i].f;
 
 if (array[i].f < low) low = array[i].f;
 
 }
 
 double interval = ((double)(high - low + 1))/bucketCount; //range of one bucket
 
 
 ArrayList<Integer> buckets[] = new ArrayList[bucketCount];
 
 for (int i = 0; i < bucketCount; i++) { //initialize buckets
 
 buckets[i] = new ArrayList();
 
 }
 
 
 
 for (int i = 0; i < array.length; i++) { //partition the input array
 
 buckets[(int)((array[i].f - low)/interval)].add(array[i].f);
 
 }
 
 
 int pointer = 0;
 
 for (int i = 0; i < buckets.length; i++) {
 
 Collections.sort(buckets[i]); //mergeSort
 
 for (int j = 0; j < buckets[i].size(); j++) { //merge the buckets
 
 array[pointer].f = buckets[i].get(j);
 
 pointer++;
 
 }
 
}
 
return array;
 
}
}