Polycarp often uses his smartphone. He has already installed n applications on it. Application with number i takes up a_i units of memory.

Polycarp wants to free at least m units of memory (by removing some applications).

Of course, some applications are more important to Polycarp than others. He came up with the following scoring system — he assigned an integer b_i to each application: 

  * b_i = 1 — regular application; 
  * b_i = 2 — important application. 



According to this rating system, his phone has b_1 + b_2 + … + b_n convenience points.

Polycarp believes that if he removes applications with numbers i_1, i_2, …, i_k, then he will free a_{i_1} + a_{i_2} + … + a_{i_k} units of memory and lose b_{i_1} + b_{i_2} + … + b_{i_k} convenience points.

For example, if n=5, m=7, a=[5, 3, 2, 1, 4], b=[2, 1, 1, 2, 1], then Polycarp can uninstall the following application sets (not all options are listed below): 

  * applications with numbers 1, 4 and 5. In this case, it will free a_1+a_4+a_5=10 units of memory and lose b_1+b_4+b_5=5 convenience points; 
  * applications with numbers 1 and 3. In this case, it will free a_1+a_3=7 units of memory and lose b_1+b_3=3 convenience points. 
  * applications with numbers 2 and 5. In this case, it will free a_2+a_5=7 memory units and lose b_2+b_5=2 convenience points. 



Help Polycarp, choose a set of applications, such that if removing them will free at least m units of memory and lose the minimum number of convenience points, or indicate that such a set does not exist.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case contains two integers n and m (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 10^9) — the number of applications on Polycarp's phone and the number of memory units to be freed.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the number of memory units used by applications.

The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 2) — the convenience points of each application.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output on a separate line: 

  * -1, if there is no set of applications, removing which will free at least m units of memory; 
  * the minimum number of convenience points that Polycarp will lose if such a set exists. 

Example

Input


5
5 7
5 3 2 1 4
2 1 1 2 1
1 3
2
1
5 10
2 3 2 3 2
1 2 1 2 1
4 10
5 1 3 4
1 2 1 2
4 5
3 2 1 2
2 1 2 1


Output


2
-1
6
4
3

Note

In the first test case, it is optimal to remove applications with numbers 2 and 5, freeing 7 units of memory. b_2+b_5=2.

In the second test case, by removing the only application, Polycarp will be able to clear only 2 of memory units out of the 3 needed.

In the third test case, it is optimal to remove applications with numbers 1, 2, 3 and 4, freeing 10 units of memory. b_1+b_2+b_3+b_4=6.

In the fourth test case, it is optimal to remove applications with numbers 1, 3 and 4, freeing 12 units of memory. b_1+b_3+b_4=4.

In the fifth test case, it is optimal to remove applications with numbers 1 and 2, freeing 5 units of memory. b_1+b_2=3.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	
//	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	Scanner sc=new Scanner(System.in);
//	int t=Integer.parseInt(bf.readLine());
    int t=sc.nextInt();
    StringBuilder sb=new StringBuilder();
	while(t-->0)
	{
	    int n=sc.nextInt();
	   
	    int m=sc.nextInt();
	    int a[]=new int[n];
	    long over=0L;
	    int b[]=new int[n];
	    for(int i=0;i<n;i++)
	 {   a[i]=sc.nextInt();
	    over=over+0L+a[i];
	}
	    
	    for(int i=0;i<n;i++)
	    b[i]=sc.nextInt();
	     if(n==1 || over<m){
	    sb.append("-1\n");
	    continue;
	}
	    ArrayList<data2> al1=new ArrayList<>();
	    ArrayList<data2> al2=new ArrayList<>();
	    ArrayList<data2> al3=new ArrayList<>();
	    
	    for(int i=0;i<n;i++)
	    {
	        if(b[i]==1)
	        {
	            double z=(a[i]*1.0)/b[i];
	            al2.add(new data2(a[i],b[i],z));
	        }
	        else
	        {
	            double z=(a[i]*1.0)/b[i];
	            al1.add(new data2(a[i],b[i],z));
	        }
	        
	        
	    }
	    
	    Collections.sort(al2,new MIN());
	    Collections.sort(al1,new MIN());
	    al1.addAll(al1);
	    al3.addAll(al2);
	    Collections.sort(al3,new MIN());
	    
	    sum=0L;
	   i1=0;
	   i2=0;
	   boolean san=false;
	    while(m>0)
	    {
	        if(al2.size()>i2  && (int)al2.get(i2).z1>=m)
	        {
	            
	            int minal=(int)al2.get(i2).z2;
	            sum=sum+0L+minal;
	             System.out.println("min1 "+" "+minal+" "+sum+" i1 i2 "+i1+" "+i2);
	            m=m-(int)al2.get(i2).z1;
	            i2++;
	        }
	        else
	        {
	            int min=takeItem(al1,al2);
	           System.out.println("min2 "+min+" "+sum+" "+m+" i1i2 "+i1+" "+i2);
	            if(min==-1)
	            {
	                san=true;
	                break;
	            }
	            
	            m=m-min;
	           
	        }
	        
	    }
	    
	    if(san )
	    sb.append("-1\n");
	    else
	    {
	        int lanim=Math.abs(m);
	        for(int i=0;i<al3.size();i++)
	        {
	            if((int)al3.get(i).z1<=lanim)
	            {
	                sum=sum-(int)al3.get(i).z2;
	            }
	            if(m<=0)
	            break;
	        }
	        sb.append(sum+"\n");
	    }
	   // sb.append(sum+"\n");
	   
	    
	}
	System.out.println(sb);
	
	}
	static class data2
	{
	    int z1,z2;
	    double z3;
	    data2(int a,int b,double c)
	    {
	        z1=a;
	        z2=b;
	        z3=c;
	    }
	}
	static int i1=0;
	static int i2=0;
	static long sum=0L;
	static class MIN implements Comparator<data2>
	{
	    public int compare(data2 min1,data2 min2)
	    {
	        double p1=(double)min1.z3;
	        double p2=(double)min2.z3;
	        if(p1<p2)
	        return 1;
	        else if(p1>p2)
	        return -1;
	        else
	        return 0;
	    }
	}
	static int takeItem(ArrayList<data2> al1,ArrayList<data2>al2)
	{
	    if(al1.size()>i1 && al2.size()<=i2)
	    {
	        int z=(int)al1.get(i1).z1;
	       
	        sum=sum+0L+(int)al1.get(i1).z2;
	         i1++;
	        return z;
	        
	        
	    }
	    else  if(al2.size()>i2 && al1.size()<=i1)
	    {
	        int z=(int)al2.get(i2).z1;
	       
	        sum=sum+0L+(int)al2.get(i2).z2;
	         i2++;
	        return z;
	        
	        
	    }
	    else  if(al1.size()<=i1 && al2.size()<=i2)
	    {
	        return -1;
	        
	        
	    }
	    else if(al1.size()>i1 && al2.size()>i2 && (double)al1.get(i1).z3>=(double)al2.get(i2).z3)
	    {
	        
	        int z=(int)al1.get(i1).z1;
	       
	        sum=sum+0L+(int)al1.get(i1).z2;
	         i1++;
	        return z;
	    }
	    else
	    {
	       
	            
	            int z=(int)al2.get(i2).z1;
	            sum=sum+0L+(int)al2.get(i2).z2;
	            i2++;
	            return z;
	        
	    }
	    
	}
}