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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.NoSuchElementException;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author MahmoudJobeel
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DCleaningThePhone solver = new DCleaningThePhone();
        solver.solve(1, in, out);
        out.close();
    }

    static class DCleaningThePhone {
        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int t = sc.nextInt();
            while (t-- > 0) {
                int n = sc.nextInt();
                int m = sc.nextInt();
                int[] arr1 = sc.nextIntArray(n);
                int[] arr2 = sc.nextIntArray(n);
                ArrayList<Integer> ones = new ArrayList<>();
                ArrayList<Integer> twos = new ArrayList<>();
                for (int i = 0; i < n; i++) {
                    if (arr2[i] == 1) ones.add(arr1[i]);
                    else twos.add(arr1[i]);
                }
                Collections.sort(ones, Collections.reverseOrder());
                Collections.sort(twos, Collections.reverseOrder());
                int total = 0, cost = 0, ans = Integer.MAX_VALUE;
                int p2 = -1;
                while (p2 + 1 < twos.size() && total < m) {
                    p2++;
                    total += twos.get(p2);
                    cost += 2;
                }
                if (total >= m) ans = Math.min(ans, cost);
                for (int p1 = 0; p1 < ones.size(); p1++) {
                    total += ones.get(p1);
                    cost++;
                    while (p2 >= 0 && total - twos.get(p2) >= m) {
                        total -= twos.get(p2);
                        p2--;
                        cost -= 2;
                    }
                    if (total >= m) ans = Math.min(ans, cost);
                }
                pw.println(ans == Integer.MAX_VALUE ? -1 : ans);
            }
        }

    }

    static class Scanner {
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;

        public Scanner(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }

        public boolean hasNextByte() {
            if (curbuf >= lenbuf) {
                curbuf = 0;
                try {
                    lenbuf = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return false;
            }
            return true;
        }

        public int readByte() {
            if (hasNextByte())
                return buffer[curbuf++];
            else
                return -1;
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        public void skip() {
            while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                curbuf++;
        }

        public boolean hasNext() {
            skip();
            return hasNextByte();
        }

        public int nextInt() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }

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

    }
}

