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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class A {
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
    static class FastWriter extends PrintWriter {
        FastWriter() {
            super(System.out);
        }

        void println(int[] array) {
            for (int i = 0; i < array.length; i++) {
                print(array[i] + " ");
            }
            println();
        }

        void println(long[] array) {
            for (int i = 0; i < array.length; i++) {
                print(array[i] + " ");
            }
            println();
        }
    }
    public static void main(String[] args){
        FastScanner in = new FastScanner();
        FastWriter out=new FastWriter();
        int t=in.nextInt();
        while(t-->0){
            int n=in.nextInt();
            int m=in.nextInt();
            int[] a=in.nextArray(n);
            int[] b=in.nextArray(n);
            ArrayList<Integer> less=new ArrayList<>();
            ArrayList<Integer> more=new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if(b[i]==1){
                    less.add(a[i]);
                }else{
                    more.add(a[i]);
                }
            }
            Collections.sort(less,Collections.reverseOrder());
            Collections.sort(more,Collections.reverseOrder());
            int i=0,j=0,cnt=0,point=0;
            int mem=0;
            while(mem<m&&cnt<n){
                if(i<less.size()){
                    if(mem+less.get(i)>=m){
                        mem+=less.get(i++);
                        point++;
                        cnt++;
                        break;
                    }
                    if(i+1<less.size()){
                        if(j<more.size()){
                            if((less.get(i)+less.get(i+1))<more.get(j)){
                                mem+=more.get(j++);
                                point+=2;
                                cnt++;
                            }else{
                                cnt++;
                                point++;
                                mem+=less.get(i++);
                            }
                        }else{
                            mem+=less.get(i++);
                            point++;
                            cnt++;
                        }
                    }else{
                        if(j<more.size()){
                            point+=2;
                            mem+=more.get(j++);
                            cnt++;
                        }else{
                            point+=1;
                            mem+=less.get(i++);
                            cnt++;
                        }
                    }
                }else {
                    mem+=more.get(j++);
                    point+=2;
                    cnt++;
                }
            }
            if(mem>=m){
                out.println(point);
            }else{
                out.println("-1");
            }
        }
        out.close();
    }
}