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

public class D {

    //template
    public static void main(String[] args) throws IOException {
        FastReader s = new FastReader();
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

        int T = s.nextInt();
        for (int u = 0; u < T; u++) {
//            System.out.println("new case");
            int n = s.nextInt();
            int m = s.nextInt();
            long[] a = new long[n + 1];
            int[] cp = new int[n + 1];
            for (int i = 1; i < n + 1; i++) {
                a[i] = s.nextInt();
            }
            for (int i = 1; i < n + 1; i++) {
                cp[i] = s.nextInt();
            }
            // push to respective array
            Long[][] mem = new Long[3][n + 1];
            int cp1Index = 0;
            int cp2Index = 0;
            for (int i = 1; i < n + 1; i++) {
                if (cp[i] == 1) {
                    mem[1][++cp1Index] = a[i];
                } else {
                    mem[2][++cp2Index] = a[i];
                }
            }
            // sort
//        System.out.println(Arrays.toString(mem[1]));
//        System.out.println(Arrays.toString(mem[2]));

            Arrays.sort(mem[1], 1, cp1Index + 1);
            Arrays.sort(mem[2], 1, cp2Index + 1);

//            System.out.println("before reversing");
//            System.out.println(Arrays.toString(mem[1]));
//            System.out.println(Arrays.toString(mem[2]));
            Long[] reverseMem1 = new Long[mem[1].length];
            Long[] reverseMem2 = new Long[mem[2].length];
            for (int i = 0; i < reverseMem1.length; i++) {
                reverseMem1[i] = 0L;
            }
            for (int i = 0; i < reverseMem2.length; i++) {
                reverseMem2[i] = 0L;
            }
            for (int i = 1; i <= cp1Index; i++) {
                reverseMem1[i] = mem[1][cp1Index + 1 - i];
            }
            for (int i = 1; i <= cp2Index; i++) {
                reverseMem2[i] = mem[2][cp2Index + 1 - i];
            }
//            System.out.println("after reversing");
            mem[1] = reverseMem1;
            mem[2] = reverseMem2;
            // make prefix sum array
            for (int i = 1; i <= cp1Index; i++) {
                mem[1][i] += mem[1][i - 1];
            }
            for (int i = 1; i <= cp2Index; i++) {
                mem[2][i] += mem[2][i - 1];
            }
//            System.out.println(Arrays.toString(mem[1]));
//            System.out.println(Arrays.toString(mem[2]));
            // start to get minimum convenient number
            // if total mem < m, return -1
            if (mem[1][cp1Index] + mem[2][cp2Index] < m) {
                System.out.println(-1);
                continue;
            }
            // m is cost
            int cp1ArrayPointer = 0;
            int cp2ArrayPointer = cp2Index;
            long limit = m;
            int best = Integer.MAX_VALUE;
//            System.out.println("limit " + limit);
//            System.out.println(Arrays.toString(mem[2]));
//            System.out.println(getLowerBound(mem[2], limit, cp2ArrayPointer));
//            System.out.println(mem[2][getLowerBound(mem[2], limit, cp2ArrayPointer)]);
            while (mem[2][getLowerBound(mem[2], limit, cp2ArrayPointer)] < limit) {
//            while (getLowerBound(mem[2], limit, cp2ArrayPointer) == cp2Index + 1) {
//                System.out.println("sum of all cp2 app less than m");
                limit = m - mem[1][++cp1ArrayPointer];
            }
            // sum from cp2 is more than enough
            // check if cp1 pointer not larger than max index
            // and cp2 pointer not less then 0
//            System.out.println("limit " + limit);
            cp2ArrayPointer = getLowerBound(mem[2], limit, cp2ArrayPointer);
            best = Math.min(best, getTotalCp(cp1ArrayPointer, cp2ArrayPointer));
//            System.out.println("best is " + best + " and getTotalCp is " + getTotalCp(cp1ArrayPointer, cp2ArrayPointer));
//            System.out.println(Arrays.toString(mem[1]));
//            System.out.println(Arrays.toString(mem[2]));
            while (cp1ArrayPointer < cp1Index && cp2ArrayPointer >= 0) {
//            System.out.println(getLowerBound(mem[2], limit, cp2ArrayPointer));
//                System.out.println("cp1 " + cp1ArrayPointer);
                limit = m - mem[1][++cp1ArrayPointer];
//                System.out.println("limit " + limit);
                cp2ArrayPointer = getLowerBound(mem[2], limit, cp2ArrayPointer);
//                System.out.println("best is " + best + " and getTotalCp is " + getTotalCp(cp1ArrayPointer, cp2ArrayPointer));
                best = Math.min(best, getTotalCp(cp1ArrayPointer, cp2ArrayPointer));
            }
            bw.write(best + "\n");
            bw.flush();
        }
        bw.close();
    }

    public static int getLowerBound(Long[] arr, long k, int endIndex) {
        int index = endIndex;
        if (index == 0) {
            return 0;
        }
        if (arr[index] < k) {
            return index + 1;
        }
        while (arr[index - 1] >= k) {
            index--;
            if (index == 0) {
                break;
            }
        }
        return index;
    }

    public static int getTotalCp(int cp1Index, int cp2Index) {
        return cp1Index + cp2Index * 2;
    }

    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;
        }
    }
}
