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 static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

public class x1475D
{
    public static void main(String hi[]) throws Exception
    {
        BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(infile.readLine());
        int T = Integer.parseInt(st.nextToken());
        StringBuilder sb = new StringBuilder();
        while(T-->0)
        {
            st = new StringTokenizer(infile.readLine());
            int N = Integer.parseInt(st.nextToken());
            int X = Integer.parseInt(st.nextToken());
            int[] arr = readArr(N, infile, st);
            int[] brr = readArr(N, infile, st);
            ArrayList<Integer> ones = new ArrayList<Integer>();
            ArrayList<Integer> twos = new ArrayList<Integer>();
            for(int i=0; i < N; i++)
            {
                if(brr[i] == 1)
                    ones.add(arr[i]);
                else
                    twos.add(arr[i]);
            }
            Collections.sort(ones);
            Collections.sort(twos);
            Collections.reverse(ones);
            Collections.reverse(twos);
            int M = ones.size();
            long[] psums = new long[M];
            if(M > 0)
            {
                psums[0] = ones.get(0);
                for(int i=1; i < M; i++)
                    psums[i] = psums[i-1]+ones.get(i);
            }
            long res = Long.MAX_VALUE;
            long prefix = 0L;
            for(int i=0; i < twos.size(); i++)
            {
                prefix += twos.get(i);
                int cost = (i+1)*2;
                if(prefix < X && M > 0)
                {
                    if(prefix+psums[M-1] < X)
                        continue;
                    int low = 0;
                    int high = M-1;
                    while(low != high)
                    {
                        int mid = (low+high)/2;
                        if(psums[mid]+prefix < X)
                            low = mid+1;
                        else
                            high = mid;
                    }
                    cost += low+1;
                    res = min(res, cost);
                }
                else if(prefix >= X)
                    res = min(res, cost);
            }
            if(M > 0 && psums[M-1] >= X)
            {
                int low = 0;
                int high = M-1;
                while(low != high)
                {
                    int mid = (low+high)/2;
                    if(psums[mid] < X)
                        low = mid+1;
                    else
                        high = mid;
                }
                res = min(res, low+1);
            }
            if(res == Long.MAX_VALUE)
                res = -1;
            sb.append(res+"\n");
        }
        System.out.print(sb);
    }
    public static int[] readArr(int N, BufferedReader infile, StringTokenizer st) throws Exception
    {
        int[] arr = new int[N];
        st = new StringTokenizer(infile.readLine());
        for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(st.nextToken());
        return arr;
    }
}
/*
5
5 7
5 3 2 1 4
2 2 2 2 2
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

 */