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.*;
import java.text.*;
import java.math.*;
import java.lang.Math.*;

public class reading_books_hard_version {
	
	public static void main(String[] args) throws Exception {new reading_books_hard_version().run();}
	public FastIO file = new FastIO();
	public int ntc, ctc;
	public final long MOD = 1000000007L; //998244353L; 
	public final int M0D = 1000000007; //998244353
	public final int N = 200005, dx[] = { 0, 1, 0, -1 }, dy[] = { 1, 0, -1, 0 };
	
	public void run() throws Exception {
		ntc = 1; //nextInt();
		for (ctc = 1; ctc <= ntc; ++ctc) solve();
		file.out.flush(); file.out.close();
	}
	
	int n, m, k, a[], b[];
	
	void add(int index, int value) {
		for(++index;index<=n;index+=index&-index) {
			a[index] += value;
			++b[index];
		}
	}
	
	void remove(int index, int value) {
		for(++index;index<=n;index+=index&-index) {
			a[index] -= value;
			--b[index];
		}
	}
	
	int get(int index) {
		int ind = 0, x = 0, y = 0;
		for (int j = 1 << 21; j > 0; j >>= 1) {
			if (ind + j <= n && x + b[ind + j] <= index) {
				ind += j;
				x += b[ind];
				y += a[ind];
			}
		}
		return y;
	}
	
	class Pair implements Comparable<Pair> {
		int fi, se;
		Pair(int x, int y) {
			fi = x; se = y;
		}
		public int compareTo(Pair o) {
			if (fi == o.fi) return se - o.se;
			return fi - o.fi;
		}
	}
	
	void solve() {
		n = nextInt();
		m = nextInt();
		k = nextInt();
		a = new int[n+1];
		b = new int[n+1];
		ArrayList<Pair> XX = new ArrayList<>(), XY = new ArrayList<>(), YX = new ArrayList<>(), YY = new ArrayList<>();
		Pair[] books = new Pair[n]; int[] mp = new int[n];
		for (int i = 0; i < n; ++i) {
			int t = nextInt(), a = nextInt(), b = nextInt();
			books[i] = new Pair(t, i);
			if (a == 1 && b == 1)
				XX.add(new Pair(t, i));
			if (a == 0 && b == 1)
				YX.add(new Pair(t, i));
			if (a == 1 && b == 0)
				XY.add(new Pair(t, i));
			if (a == 0 && b == 0)
				YY.add(new Pair(t, i));
		}
		if (XX.size() + min(YX.size(), XY.size()) < k) {
			println(-1); return;
		}
		Arrays.sort(books);
		for (int i = 0; i < n; ++i)
			mp[books[i].se] = i;
		Collections.sort(XX);
		Collections.sort(XY);
		Collections.sort(YX);
		Collections.sort(YY);
		for (Pair p : XX) 
			add(mp[p.se], p.fi);
		for (Pair p : XY) 
			add(mp[p.se], p.fi);
		for (Pair p : YX) 
			add(mp[p.se], p.fi);
		for (Pair p : YY) 
			add(mp[p.se], p.fi);
		int ans = Integer.MAX_VALUE, sum = 0, num = 0, bi = XX.size();
		for (Pair p : XX) {
			++num; sum += p.fi;
			remove(mp[p.se], p.fi);
		}
		for (int i = 0; i < k - XX.size(); ++i) {
			num += 2; sum += XY.get(i).fi + YX.get(i).fi;
			remove(mp[XY.get(i).se], XY.get(i).fi);
			remove(mp[YX.get(i).se], YX.get(i).fi);
		}
		if (num <= m)
			ans = sum + get(m - num);
		for (int i = XX.size() - 1; i >= 0; --i) {
			--num; sum -= XX.get(i).fi;
			add(mp[XX.get(i).se], XX.get(i).fi);
			if (i < k) {
				if (k - i > min(XY.size(), YX.size()))
					break;
				num += 2; sum += XY.get(k - i - 1).fi + YX.get(k - i - 1).fi;
				remove(mp[XY.get(k - i - 1).se], XY.get(k - i - 1).fi);
				remove(mp[YX.get(k - i - 1).se], YX.get(k - i - 1).fi);
			}
			int cur = sum + get(m - num);
			if (cur < ans && m >= num) {
				ans = cur;
				bi = i;
			}
		}
		num = m;
		if (ans == Integer.MAX_VALUE) {
			println(-1); return;
		}
		println(ans);
		PriorityQueue<Pair> pq = new PriorityQueue<>();
		for (int i = 0; i < XX.size(); ++i)
			if (i < bi) {
				--num;
				print((1+XX.get(i).se) + " ");
			}
			else
				pq.add(XX.get(i));
		for (int i = 0; i < XY.size(); ++i)
			if (i < k - bi) {
				--num;
				print((1+XY.get(i).se) + " ");
			}
			else
				pq.add(XY.get(i));
		for (int i = 0; i < YX.size(); ++i)
			if (i < k - bi) {
				--num;
				print((1+YX.get(i).se) + " ");
			}
			else
				pq.add(YX.get(i));
		for (Pair p : YY)
			pq.add(p);
		while (num-- > 0)
			print((1+pq.poll().se) + " ");
		println("");
	}
	
	void sort(long[] a) { shuffle(a); Arrays.sort(a); }
	void sort(int[] a) { shuffle(a); Arrays.sort(a); }
	void shuffle(long[] a) {
		for (int i = a.length - 1; i >= 0; i--) { int j = (int) (Math.random() * (i + 1)); a[i] ^= a[j] ^ (a[j] = a[i]); } }
	void shuffle(int[] a) {
		for (int i = a.length - 1; i >= 0; i--) { int j = (int) (Math.random() * (i + 1)); a[i] ^= a[j] ^ (a[j] = a[i]); } }
	long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
	long lcm(long x, long y) { return x / gcd(x, y) * y; }
	long mod(long n, long mod) { return (n % mod + mod) % mod; }
	long max(long a, long b) { return Math.max(a, b); }
	int max(int a, int b) { return Math.max(a, b); }
	long min(long a, long b) { return Math.min(a, b); }
	int min(int a, int b) { return Math.min(a, b); }
	long pow(long n, long p, long mod) { long ret = 1L;
	while (p > 0) { if (p % 2 != 0L) ret = mod(ret * n, mod); n = mod(n * n, mod); p >>= 1L; } return ret; }
	long pow(long n, long p) { long ret = 1L;
	while (p > 0) { if (p % 2 != 0L) ret *= n; n *= n; p >>= 1L; } return ret; }
	boolean isPrime(int n) { 
		if (n <= 1) return false; if (n <= 3) return true; if (n % 2 == 0 || n % 3 == 0) return false;
		for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return false; return true; }
	String next() {return file.next();}
	int nextInt() {return file.nextInt();}
	long nextLong() {return file.nextLong();}
	double nextDouble() {return file.nextDouble();}
	String nextLine() {return file.nextLine();}
	void print(Object o) {file.out.print(o);}
	void println(Object o) {file.out.println(o);}
	void printf(String s, Object... o) {file.out.printf(s, o);}
	class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;
		public FastIO() {br = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);}
		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;}
		void print(Object o) {out.print(o);}
		void println(Object o) {out.println(o);}
		void printf(String s, Object... o) {out.printf(s, o);} } }