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.
/**
 *
 * @author Harshwardhan Yadav
 */
import java.math.*;
import java.io.*;
import java.util.*;
public class Codeforces {

    /**
     * @param args the command line arguments
     */
    //matrix eight directions conditions
    /*if(p.x>1 && p.y>1 && board[p.x-1][p.y-1]!=1)
                {
                    q.add(new pair(p.x-1,p.y-1));
                }
                if(p.x>1 && board[p.x-1][p.y]!=1){
                    q.add(new pair(p.x-1,p.y));
                }
                if(p.x>1 && p.y<n && board[p.x-1][p.y+1]!=1){
                    q.add(new pair(p.x-1,p.y+1));
                }
                if(p.y>1 && board[p.x][p.y-1]!=1){
                    q.add(new pair(p.x,p.y-1));
                }
                if(p.y<n && board[p.x][p.y+1]!=1){
                    q.add(new pair(p.x,p.y+1));
                }
                if(p.x<n && p.y>1 && board[p.x+1][p.y-1]!=1){
                    q.add(new pair(p.x+1,p.y-1));
                }
                if(p.x<n && board[p.x+1][p.y]!=1){
                    q.add(new pair(p.x+1,p.y));
                }
                if(p.x<n && p.y<n && board[p.x+1][p.y+1]!=1){
                    q.add(new pair(p.x+1,p.y+1));
                }
            }*/
    static class Valueable{
        int x;
        int y;
        Valueable(int ch,int pos)
        {
            this.x=ch;
            this.y=pos;
        }
    }

    static class Sortbyroll implements Comparator<Valueable> 
    { 
        // Used for sorting in ascending order of 
        // roll number 
        @Override
        public int compare(Valueable a,Valueable b)
        {
            return a.x-b.x;
        }
    }

    static int findMaxElementIndex(int ar[])
    {
        int index=0;
        int max=0;
        int n=ar.length;
        for(int i=0;i<n;i++)
        {
            if(ar[i]>max)
            {
                max=ar[i];
                index=i;
            }
        }
        return index;
    }

    static int findMaxElement(int ar[])
    {
        int max=0;
        int n=ar.length;
        for(int i=0;i<n;i++)
        {
            if(ar[i]>max)
            {
                max=ar[i];
            }
        }
        return max;
    }

    static int binarySearch(String s,String q,int p[],int start,int end)
    {
        int mid=(start+end)/2;
        int result=-1;
        int n=s.length();
        if(start<=end)
        {
            int x=0;
            if(x==0)
            {
                return mid;
            }
            else if(x<0)
            {
                result=binarySearch(s, q, p,mid+1, end);
            }
            else{
                result=binarySearch(s, q, p,start, mid-1);
            }
        }
        else{
            return -1;
        }
        return result;
    }
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
 
        public FastReader() 
        { 
            br = new BufferedReader(new
                    InputStreamReader(System.in)); 
        } 
 
        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; 
        }
        
        int[] nextIntArray(int n)
        {
            int arr[]=new int[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }

        Integer[] nextIntegerArray(int n)
        {
            Integer arr[]=new Integer[n];
            for(Integer i=0;i<n;i++)
            {
                arr[i]=Integer.parseInt(next());
            }
            return arr;
        }

        long[] nextLongArray(int n)
        {
            long arr[]=new long[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=Long.parseLong(next());
            }
            return arr;
        }

    } 
 
    static int gcd(Integer a,Integer b)
    {
        if(b==0)
            return a;
        else
            return gcd(b,a%b);
    }
 
    static boolean checkForPrime(long inputNumber)
    {
        boolean isItPrime = true;
        if(inputNumber <= 1) 
        {
            isItPrime = false;
            return isItPrime;
        }
        else
        {
            if(inputNumber%2==0 && inputNumber==2)
            {
                return true;
            }
            else if(inputNumber%2==0)
            {
                return false;
            }
            else{
                int check=(int)Math.sqrt(inputNumber);
                for (int i = 3; i<= check; i+=2) 
                {
                    if ((inputNumber % i) == 0)
                    {
                        isItPrime = false;
                        break;
                    }
                }
            }
        }
 
        return isItPrime;
    } 
    
    /*static SortedSet<Valueable> ts=new TreeSet<Valueable>(new Comparator<Valueable>(){
        @Override
        public int compare(Valueable a,Valueable b)
        {
            if(a.r-a.l==b.r-b.l)
            {
                return a.l-b.l;
            }
            else{
                return (-1)*((a.r-a.l)-(b.r-b.l));
            }
        }
    }
    );*/
    
    static void countSort(int p[], int n, int exp,int[] c) 
    { 
        int output[] = new int[n]; 
        int i; 
        int count[] = new int[10]; 
        Arrays.fill(count, 0);  
        for (i = 0; i < n; i++) 
            count[(c[p[i]] / exp) % 10]++;
        for (i = 1; i < 10; i++) 
            count[i] += count[i - 1]; 
        for (i = n - 1; i >= 0; i--) { 
            output[count[(c[p[i]] / exp) % 10] - 1] = p[i]; 
            count[(c[p[i]] / exp) % 10]--; 
        } 
        for (i = 0; i < n; i++) 
            p[i] = output[i]; 
    } 
  
    /*static void radixsort(int p[], int[] c) 
    { 
        int m = getMax(p,p.length); 
        for (int exp = 1; m / exp > 0; exp *= 10) 
            countSort(p, p.length, exp,c); 
    }*/
    
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException {
        // TODO code application logic here
        FastReader sc=new FastReader();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        int t=sc.nextInt();
        for(int test=0;test<t;test++)
        {
            int n=sc.nextInt(),m=sc.nextInt();
            int[] a=sc.nextIntArray(n);
            int[] b=sc.nextIntArray(n);
            int count=0;
            int lost=0;
            ArrayList<Integer> l1=new ArrayList<Integer>();
            ArrayList<Integer> l2=new ArrayList<Integer>();
            for(int i=0;i<n;i++)
            {
                if(b[i]==1)
                    l1.add(a[i]);
                else
                    l2.add(a[i]);
                count+=a[i];
            }
            Collections.sort(l1);
            Collections.sort(l2);
            if(count<m)
                out.write("-1\n");
            else{
                count=0;
                int i=l1.size()-1,j=l2.size()-1;
                while(i>=0 && j>=0 && count<m){
                    
                    if(l1.get(i)>=l2.get(j)){
                        count+=l1.get(i);
                        lost++;
                        i--;
                    }
                    else{
                        count+=l2.get(j);
                        lost+=2;
                        j--;
                    }
                }
                while(i>=0 && count<m){
                     count+=l1.get(i);
                        lost++;
                        i--;
                }
                while(j>=0 && count<m){
                    count+=l2.get(j);
                        lost+=2;
                        j--;
                }
                while(i>=0 && j<l2.size()-1 && count-l2.get(j+1)+l1.get(i)>=m){
                    count=count-l2.get(j+1)+l1.get(i);
                    lost--;
                    i--;
                }
                out.write(lost+"\n");
            }
            out.flush();
        }    
        out.close();
    }
    
}
