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.math.*;
import java.io.*; 
 public class A{
 
static FastReader scan=new FastReader();
 public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static LinkedList<Integer>edges[];
 // static LinkedList<Pair>edges[];
  static boolean stdin = true;
    static String filein = "input";
    static String fileout = "output";
static int dx[] = { -1, 0, 1, 0 };
static int dy[] = { 0, 1, 0, -1 };
int dx_8[]={1,1,1,0,0,-1,-1,-1};
int dy_8[]={-1,0,1,-1,1,-1,0,1};
static char sts[]={'U','R','D','L'};
static boolean prime[];
static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
    public static int upperBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = low+(high-low) / 2;
            if ( array[mid]>value) {
                high = mid ;
            } else {
                low = mid+1;
            }
        }
        return low;
    }
   static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
static int countSetBits(int n) 
    { 
        int count = 0; 
        while (n > 0) { 
            if((n&1)!=1)
                count++;
            //count += n & 1; 
            n >>= 1; 
        } 
        return count; 
    } 
 static void sieve(long n) 
    { 
        
        prime = new boolean[(int)n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
           
            if(prime[p] == true) 
            { 
                
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }  
  
 
 
           static boolean isprime(long x)
           {
            for(long i=2;i*i<=x;i++)
                if(x%i==0)
                    return false;
                return true;
           }
           static int perm=0,FOR=0;
           
     
 
static boolean flag=false;
static int len=100000000;
 
static ArrayList<Pair>inters=new ArrayList<Pair>();
 
  
static class comp1 implements  Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
return  Integer.compare((int)o2.x,(int)o1.x);
}
  }
  public static class comp2 implements Comparator<Pair>{  
public int compare(Pair o1,Pair o2){
return Integer.compare((int)o2.x,(int)o1.x); 
}
  }
  static StringBuilder a,b;
 
    static boolean isPowerOfTwo(int n)
{
    if(n==0)
    return false;
 
return (int)(Math.ceil((Math.log(n) / Math.log(2)))) == 
       (int)(Math.floor(((Math.log(n) / Math.log(2)))));
}
static ArrayList<Integer>v;
static ArrayList<Integer>pows;
static void block(long x) 
{ 
   v = new ArrayList<Integer>(); 
      
    pows=new ArrayList<Integer>();
   
    while (x > 0)  
    { 
        v.add((int)x % 2); 
        x = x / 2; 
    } 
  
    // Displaying the output when 
    // the bit is '1' in binary 
    // equivalent of number. 
    for (int i = 0; i < v.size(); i++)  
    { 
        if (v.get(i)==1)  
        { 
      pows.add(i); 
        } 
    } 
 
} 
 
 
   static long ceil(long a,long b)
   {
    if(a%b==0)
        return a/b;
    return a/b+1;
   }
 


static boolean isprime(int n)
    {
        // Corner cases
        if (n <= 1) return false;
        if (n <= 3) return true;
         
        // This is checked so that we can skip
        // middle five numbers in below loop
        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;
    }
     
    // Function to return the smallest
    // prime number greater than N
    static int nextPrime(int N)
    {
     
        // Base case
        if (N <= 1)
            return 2;
     
        int prime = N;
        boolean found = false;
     
        // Loop continuously until isPrime returns
        // true for a number greater than n
        while (!found)
        {
            prime++;
     
            if (isprime(prime))
                found = true;
        }
     
        return prime;
    }
  
    
    static long mod=(long)1e9+7;
static int mx=0,k;

static long nPr(long n,long r)
{
    
    long ret=1;
    for(long i=n-r+1;i<=n;i++)
    {
       ret=1L*ret*i%mod;
           }
    return ret%mod;
}

   
public static void main(String[] args)  throws Exception 
{
//SUCK IT UP AND DO IT ALRIGHT
//scan=new FastReader("hps.in");
//out = new PrintWriter("hps.out");
   //System.out.println( 1005899102^431072812);
    //int elem[]={1,2,3,4,5};
//System.out.println("avjsmlfpb".compareTo("avjsmbpfl"));
int tt=1;

/*for(int i=0;i<=100;i++)
    if(prime[i])
        arr.add(i);
    System.out.println(arr.size());*/
   // check(new StringBuilder("05:11"));
   // System.out.println(26010000000000L%150);
 //System.out.println((1000000L*99000L));
 //tt=scan.nextInt();
  //  System.out.println(2^6^4);
    //StringBuilder o=new StringBuilder("GBGBGG");
    //o.insert(2,"L");
 int T=tt;

 //System.out.println(gcd(3,gcd(24,gcd(120,168))));
//System.out.println(gcd(40,gcd(5,5)));
//System.out.println(gcd(45,gcd(10,5)));

//System.out.println(primes.size());

outer:while(tt-->0)
{
  int n=scan.nextInt(),k=scan.nextInt();
  ArrayList<Integer>first=new ArrayList<Integer>();
  ArrayList<Integer>second=new ArrayList<Integer>();
  ArrayList<Integer>third=new ArrayList<Integer>();
  for(int i=0;i<n;i++)
  {
    int t=scan.nextInt(),a=scan.nextInt(),b=scan.nextInt();
    if(a==1&&b==1)
        first.add(t);
    else if(a==1&&b==0)
        second.add(t);
    else if(a==0&&b==1)
        third.add(t);
  }
  Collections.sort(second);
  Collections.sort(first);
  Collections.sort(third);
  if(first.size()+second.size()<k||first.size()+third.size()<k)
  {
    out.println(-1);
    out.close();
    return;
  }
  int res=0;
  if(first.size()==0)
  {
    for(int i=0;i<k;i++)
        res+=second.get(i);
    for(int i=0;i<k;i++)
        res+=third.get(i);
    out.println(res);
    out.close();
    return;
  }
  if(first.size()<k)
  {
        int tmpk=k;
        for(int i=0;i<first.size();i++)
  {
    res+=first.get(i);
    tmpk--;
  }
  for(int i=0;i<tmpk;i++)
  {
    res+=second.get(i);
    res+=third.get(i);
  }

  int l=tmpk,r=tmpk;
  /*if(n==200000 &&k==70874)
{
    out.println("FUCK");
    out.println(res);
}*/
  for(int i=first.size()-1;i>=0;i--)
  {
    if(l<second.size()&&r<third.size()&&second.get(l)+third.get(r)<first.get(i)){
        res-=first.get(i);
    res+=(second.get(l)+third.get(r));
    l++;
    r++;
}
else break;
  }
  out.println(res);
  out.close();
  return;
  }

  for(int i=0;i<Math.min(first.size(),k);i++)
  {
    res+=first.get(i);
  }
  int l=0,r=0;
  for(int i=k-1;i>=0;i--)
  {
    if(l<second.size()&&r<third.size()&&second.get(l)+third.get(r)<first.get(i))
    {
        res-=first.get(i);
       res+=second.get(l)+third.get(r);
       l++;
       r++;
    }
  }
  out.println(res);
}









out.close();
 
//SEE UP 
 
}
static class special implements Comparable<special>{
    int x,y,z,h;
    String s;
    special(int x,int y,int z,int h)
    {
        this.x=x;
        this.y=y;
        this.z=z;
        this.h=h;
    }
 
 @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            special t = (special)o;
            return t.x == x && t.y == y&&t.s.equals(s);
        }
 
public int compareTo(special o)
{
    return Integer.compare(x,o.x);
}
}
static long binexp(long a,long n)
{
    if(n==0)
        return 1;
    long res=binexp(a,n/2);
    if(n%2==1)
        return res*res*a;
    else 
        return res*res;
}
 
static long powMod(long base, long exp, long mod) {
       if (base == 0 || base == 1) return base;
       if (exp == 0) return 1;
       if (exp == 1) return (base % mod+mod)%mod;
       long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
       R *= R;
       R %= mod;
       if ((exp & 1) == 1) {
           return (base * R % mod+mod)%mod;
       }
       else return (R %mod+mod)%mod;
   }
static double dis(double x1,double y1,double x2,double y2)
{
    return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
static long mod(long x,long y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }
private static void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for (long object : arr) list.add(object);
        Collections.sort(list);
    //Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
private static void sort2(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
    Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        FastReader(String filename)throws Exception
        {
 
            br=new BufferedReader(new FileReader(filename));
        }
 
        boolean hasNext(){
            String line;
            while(root.hasMoreTokens())
                return true;
            return false;
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
 static class Pair implements Comparable<Pair>{
        public long x, y;
        public Pair(long x1, long y1) {
            x=x1;
            y=y1;
        }
        @Override
        public int hashCode() {
            return (int)(x + 31 * y);
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
public int compareTo(Pair o)
{
    return (int)(o.x-x);
 
    }
 
}
 static class tuple{
        int x,y,z;
        tuple(int a,int b,int c){
            x=a;
            y=b;
            z=c;
        }
    }
    static class Edge{
        int d,w;
        Edge(int d,int w)
        {
            this.d=d;
            this.w=w;
        }
    }
}