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 Main {
 
	public static void main(String[] args) throws IOException,InterruptedException{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
		PriorityQueue<pair> pq1=new PriorityQueue<>();
		PriorityQueue<pair> pq2=new PriorityQueue<>();
		PriorityQueue<pair> pq3=new PriorityQueue<>();
		PriorityQueue<pair> pq4=new PriorityQueue<>();
		TreeSet<pair> pq5=new TreeSet<>();
		TreeSet<pair> pq6=new TreeSet<>();
		TreeSet<pair> pq7=new TreeSet<>();
		TreeSet<pair> pq8=new TreeSet<>();
		for (int i = 0; i < n; i++) {
			int t=sc.nextInt(),a=sc.nextInt(),b=sc.nextInt();
			if(a==1&&b==1) {
				pq1.add(new pair(t,i+1));
			}else if(a==1) {
				pq2.add(new pair(t,i+1));
			}else if(b==1) {
				pq3.add(new pair(t,i+1));
			}else {
				pq4.add(new pair(t,i+1));
			}
		}
		long c=0;
		for (int i = 0; i < k; i++) {
			long a=1000000000;
			long b=1000000000;
			if(!pq1.isEmpty()) a=pq1.peek().x;
			if(!pq2.isEmpty()&&!pq3.isEmpty()) b=pq2.peek().x+pq3.peek().x;
			if (a==1000000000&&b==1000000000) {
				c=-1;
				break;
			}
			if(a<=b) {
				c+=a;
				pq5.add(pq1.poll());
			}else {
				c+=b;
				pq6.add(pq2.poll());
				pq7.add(pq3.poll());
			}
		}
		if (pq5.size()+pq6.size()+pq7.size()>m) {
			while (pq5.size()+pq6.size()+pq7.size()>m) {
				if(pq1.isEmpty()) {
					c=-1;
					break;
				}
				c-=pq7.pollLast().x;
				c-=pq6.pollLast().x;
				c+=pq1.peek().x;
				pq5.add(pq1.poll());
			}
		}else if (pq5.size()+pq6.size()+pq7.size()+pq8.size()<m) {
			int c3=0,c2=0;
			while (pq5.size()+pq6.size()+pq7.size()+pq8.size()<m) {
				pair a=new pair(1000000000,1000000000);
				boolean f1=false,f2=false,f3=false;
				if(!pq1.isEmpty()) {
					a=pq1.poll();
					f1=true;
				}
				if(!pq2.isEmpty())
					if (pq2.peek().x<=a.x) {
						if(f1) pq1.add(a);
						a=pq2.poll();
						f2=true;
						f1=false;
					} 
				if(!pq3.isEmpty()) 
					if (pq3.peek().x<=a.x) {
						if(f1) pq1.add(a);
						else if(f2) pq2.add(a);
						a=pq3.poll();
						f3=true;
						f2=false;
						f1=false;
					} 
				if(!pq4.isEmpty()) 
					if (pq4.peek().x<=a.x) {
						if(f1)pq1.add(a);
						else if(f2) pq2.add(a);
						else if(f3) pq3.add(a);
						a=pq4.poll();
						f3=false;
						f2=false;
						f1=false;
					}
				if(f2) c2++;
				if(f3) c3++;
				if(c2>=1&&c3>=1&&!pq5.isEmpty()) {
					c2--;
					c3--;
					c-=pq5.last().x;
					pq1.add(pq5.pollLast());
				}else if (c2>=1&&!pq3.isEmpty()&&!pq5.isEmpty()) {
					if (pq3.peek().x<pq5.last().x) {
						c2--;
						c-=pq5.last().x;
						c+=pq3.peek().x;
						pq1.add(pq5.pollLast());
						pq7.add(pq3.poll());
					}
				}else if (c3>=1&&!pq2.isEmpty()&&!pq5.isEmpty()) {
					if (pq2.peek().x<pq5.last().x) {
						c2--;
						c-=pq5.last().x;
						c+=pq2.peek().x;
						pq1.add(pq5.pollLast());
						pq6.add(pq2.poll());
					}
				}
				if(f1) pq5.add(a);
				else if(f2) pq6.add(a);
				else if(f3) pq7.add(a);
				else pq8.add(a);
				c+=a.x;
			}
		}
		if(pq5.size()+pq6.size()<k||pq5.size()+pq7.size()<k)  c=-1;
		pw.println(c);
		if(c!=-1) {
			while (!pq5.isEmpty()) {
				pw.print(pq5.pollFirst().y+" ");
			} while (!pq6.isEmpty()) {
				pw.print(pq6.pollFirst().y+" ");
			} while (!pq7.isEmpty()) {
				pw.print(pq7.pollFirst().y+" ");
			} while (!pq8.isEmpty()) {
				pw.print(pq8.pollFirst().y+" ");
			} 
			pw.println();
		}
		pw.close();
    }
	
	static PrintWriter pw=new PrintWriter(System.out);
	static long pow(int a,int b) {
		long r=1l;
		for (int i = 0; i < b; i++) {
			r*=a;
		}
		return r;
	}
	static boolean isprime(long n) {
		for (int i = 2; i <= Math.sqrt(n); i++) {
			if(n%i==0) return false;
		}
		return true;
	}
	static int[]lp;
	static void sieveLinear(int N){
		ArrayList<Integer> primes = new ArrayList<Integer>();
		lp = new int[N + 1];								//lp[i] = least prime divisor of i
		for(int i = 2; i <= N; ++i){
			if(lp[i] == 0){
				primes.add(i);
				lp[i] = i;
			}
			int curLP = lp[i];
			for(int p: primes)//all primes smaller than or equal my lowest prime divisor
				if(p > curLP || p * 1l * i > N)
					break;
				else
					lp[p * i] = p;
		}
	}
	static long gcd(int x,int y) {
		while (x!=y) {
			if(Math.max(x,y)/Math.min(x,y)==(double)(Math.max(x,y))/Math.min(x,y)) return Math.min(x,y);
			if(lp.length!=0) {
				if(lp[x]==x) {
					if(y/x==y/(double)x) return x;
					else return 1;
				}else if (lp[y]==y) {
					if(x/y==x/(double)y) return y;
					else return 1;
				}	
			}
			if(x>y) x-=y;
			else y-=x;
		}
		return x;
	}
	static class pair implements Comparable<pair> {
		int x;
		int y;
 
		public pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
 
		public String toString() {
			return x + " " + y;
		}
		public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair)o;
                return p.x == x && p.y == y;
            }
            return false;
        }
        public int hashCode() {
            return new Double(x).hashCode() * 31 + new Double(y).hashCode();
        }
        public int compareTo(pair other) {
        	if(this.x==other.x) {
        		return Long.compare(this.y, other.y);
        	}
			return Long.compare(this.x, other.x);
		}
	}
	static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;
 
		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int compareTo(tuble other) {
			if (this.x == other.x) {
				if(this.y==other.y) return this.z - other.z;
				else return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}
 	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public boolean hasNext() {
			// TODO Auto-generated method stub
			return false;
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
	}
 
}