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.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;
public class Main12{
	static public void main(String args[])throws IOException{
		int tt=1;
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++){
			int n=i();
			int k=i();
			int[] a=new int[n];
			int[] b=new int[n];
			int[] c=new int[n];
			Pair[] pair=new Pair[n];
			ArrayList<Integer> alice=new ArrayList<>();
			ArrayList<Integer> bob=new ArrayList<>();
			ArrayList<Integer> both=new ArrayList<>();
			for(int i=0;i<n;i++){
				a[i]=i();
				b[i]=i();
				c[i]=i();
				if(b[i]==1 && c[i]==1){
					both.add(a[i]);
				}else if(b[i]==1){
					alice.add(a[i]);
				}else if(c[i]==1){
					bob.add(a[i]);
				}
			}
			Collections.sort(both);
			Collections.sort(bob);
			Collections.sort(alice);
			int[] pre=new int[bob.size()+1];
			if(bob.size()>0){
			pre[0]=bob.get(0);
			for(int i=1;i<bob.size();i++){
				pre[i]=pre[i-1]+bob.get(i);
			}}
			long[] pp=new long[alice.size()+1];
			if(alice.size()>0){
			pp[0]=alice.get(0);
			for(int i=1;i<alice.size();i++){
				pp[i]=pp[i-1]+alice.get(i);
			}}
			long[] sum=new long[both.size()+1];
			if(both.size()>0){
			sum[0]=both.get(0);
			for(int i=1;i<both.size();i++){
				sum[i]=sum[i-1]+both.get(i);
			}
			}
			long min=Long.MAX_VALUE;
			for(int i=0;i<=both.size();i++){
				int taken=i;
				long ans=0;
				if(taken-1>=0){
					ans=sum[taken-1];
				}
				int remBob=k-taken;
				int remAlice=k-taken;
				if(remBob<=0){
					remBob=0;
				}
				if(remAlice<=0){
					remAlice=0;
				}
				if(remBob>bob.size()){
					continue;
				}
				if(remAlice>alice.size()){
					continue;
				}
				if(remBob>0){
					ans=ans+pre[remBob-1];
				}
				if(remAlice>0){
					ans=ans+pp[remAlice-1];
				}
				min=Math.min(ans,min);
			}
			if(min==Long.MAX_VALUE){
				sb.append("-1\n");
			}else{
				sb.append(min+"\n");
			}
		}
		System.out.print(sb.toString());
	}
	
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	static ArrayList<ArrayList<Integer>> graph;
	static int mod=1000000007;
	static class Pair{
		int x;
		int y;
		Pair(int x,int y){
			this.x=x;
			this.y=y;
		}
	/*	@Override
		public int hashCode() 
		{ 
			final int temp = 14; 
			int ans = 1; 
			ans =x*31+y*13; 
			return (int)ans;
		}*/ 
   /*    @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        }*/
	}
	public static int[] sort(int[] a){
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++){
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++){
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b){
        long result=1;
        while(b>0){
            if (b % 2 != 0){
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	public static long gcd(long a, long b){
        if (a == 0){
            return b;
		}
        return gcd(b%a, a);
    }
	public static long lcm(long a, long b){
		return a*(b/gcd(a,b));
	}
	public static long l(){
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value){
		System.out.println(value);
	}
	public static int i(){
		return in.Int();
	}
	public static String s(){
		return in.String();
	}
} 
class InputReader 
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	public InputReader(InputStream stream) {
		this.stream = stream;
	}
	public int read() {
		if (numChars== -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
	public int Int() {
		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 String String() {
		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 boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	} 
	public String next() {
		return String();
	} 
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
class OutputWriter {
	private final PrintWriter writer;
	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}
	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}
	public void close() {
		writer.close();
	}
	public void flush() {
		writer.flush();
	}
 }
class IOUtils {
	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.Int();
		return array;
	}
}