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.
import java.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=input.nextInt();
        while(T-->0)
        {
            int n,m;
            n=input.nextInt();
            m=input.nextInt();
            int a[]=new int[n];
            long sum=0;
            for(int i=0;i<n;i++)
            {
                a[i]=input.nextInt();
                sum+=a[i];
            }
            int b[]=new int[n];
            ArrayList<Integer> ones=new ArrayList<>();
            ArrayList<Integer> twos=new ArrayList<>();
            for(int i=0;i<n;i++)
            {
                b[i]=input.nextInt();
                if(b[i]==1)
                {
                    ones.add(a[i]);
                }
                else
                {
                    twos.add(a[i]);
                }
            }
            if(sum<m)
            {
                out.println(-1);
            }
            else
            {
                mergeSort(ones,0,ones.size()-1);
                mergeSort(twos,0,twos.size()-1);
                if(ones.size()!=0 && twos.size()==0)
                {
                    long s=0;
                    for(int i=0;i<ones.size();i++)
                    {
                        s+=ones.get(i);
                        if(s>=m)
                        {
                            out.println((i+1));
                            break;
                        }
                    }
                }
                else if(ones.size()==0 && twos.size()!=0)
                {
                    long s=0;
                    for(int i=0;i<twos.size();i++)
                    {
                        s+=twos.get(i);
                        if(s>=m)
                        {
                            out.println((i+1)*2);
                            break;
                        }
                    }
                }
                else
                {
                    long p1[]=new long[ones.size()];
                    long p2[]=new long[twos.size()];
                    for(int i=0;i<ones.size();i++)
                    {
                        if(i==0)
                        {
                            p1[i]=ones.get(i);
                        }
                        else
                        {
                            p1[i]=p1[i-1]+ones.get(i);
                        }
                    }
                    for(int i=0;i<twos.size();i++)
                    {
                        if(i==0)
                        {
                            p2[i]=twos.get(i);
                        }
                        else
                        {
                            p2[i]=p2[i-1]+twos.get(i);
                        }
                    }
                    int x=-1,y=-1;
                    long s=0;
                    for(int i=1;i<=2*twos.size()+ones.size();i++)
                    {
                        if((x+1<ones.size()) && (x-1>=-1 && y+1<twos.size()))
                        {
                            long s1=p1[x+1];
                            if(y>=0)
                            {
                                s1+=p2[y];
                            }
                            long s2=p2[y+1];
                            if(x-1>=0)
                            {
                                s2+=p1[x-1];
                            }
                            if(s1>s2)
                            {
                                s=s1;
                                x++;
                            }
                            else
                            {
                                s=s2;
                                x--;
                                y++;
                            }
                        }
                        else if(x+1<ones.size())
                        {
                            long s1=p1[x+1];
                            if(y>=0)
                            {
                                s1+=p2[y];
                            }
                            x++;
                            s=s1;
                        }
                        else if(x-1>=-1 && y+1<twos.size())
                        {
                            long s1=p2[y+1];
                            if(x-1>=0)
                            {
                                s1+=p1[x-1];
                            }
                            y++;
                            x--;
                            s=s1;
                        }
                        else
                        {
                            break;
                        }
                        if(s>=m)
                        {
                            out.println(i);
                            break;
                        }
                    }
                }
            }
        }
        out.close();
    }
    public static void mergeSort(ArrayList<Integer> a,int p,int r)
    {
        if(p<r)
        {
            int q=(p+r)/2;
            mergeSort(a,p,q);
            mergeSort(a,q+1,r);
            merge(a,p,q,r);
        }
    }
    public static void merge(ArrayList<Integer> a,int p,int q,int r)
    {
        int n1=q-p+2;
        int L[]=new int[n1];
        int n2=r-q+1;
        int R[]=new int[n2];
        for(int i=p;i<=q;i++)
        {
            L[i-p]=a.get(i);
        }
        L[n1-1]=Integer.MIN_VALUE;
        for(int i=q+1;i<=r;i++)
        {
            R[i-q-1]=a.get(i);
        }
        R[n2-1]=Integer.MIN_VALUE;
        int x=0,y=0;
        for(int i=p;i<=r;i++)
        {
            if(L[x]>=R[y])
            {
                a.set(i,L[x]);
                x++;
            }
            else
            {
                a.set(i,R[y]);
                y++;
            }
        }
    }
    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;
        }
    }
}