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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class Solution {
    public static void main(String[] args) {
        //noinspection IOResourceOpenedButNotSafelyClosed
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            int n = scanner.nextInt();
            int m = scanner.nextInt();
            int[] memories = new int[n];

            for (int j = 0; j < n; j++) {
                memories[j] = scanner.nextInt();
            }
            List<Integer> importantApplications = new ArrayList<>(n);
            List<Integer> nonImportantApplications = new ArrayList<>(n);
            for (int j = 0; j < n; j++) {
                boolean important = scanner.nextInt() == 2;
                if (important) {
                    importantApplications.add(memories[j]);
                } else {
                    nonImportantApplications.add(memories[j]);
                }
            }

            System.out.println(solve(nonImportantApplications, importantApplications, m));
        }
    }

    public static class Application implements Comparable<Application> {
        private final boolean important;
        private final int memory;

        public Application(boolean important, int memory) {
            this.important = important;
            this.memory = memory;
        }

        public boolean isImportant() {
            return important;
        }

        public int getMemory() {
            return memory;
        }

        @Override
        public int compareTo(Application o) {
            if (isImportant() != o.isImportant()) {
                if (isImportant()) {
                    return 1;
                } else {
                    return -1;
                }
            }
            if (getMemory() > o.getMemory()) {
                return -1;
            } else if (getMemory() < o.getMemory()) {
                return 1;
            } else {
                return 0;
            }
        }
    }


    public static long solve(List<Integer> nonImportantApplications, List<Integer> importantApplications, int requiredMemory) {
        if (requiredMemory == 0) {
            return 0;
        }
        nonImportantApplications.sort(Comparator.comparing(it -> (int) it).reversed());
        importantApplications.sort(Comparator.comparing(it -> (int) it).reversed());

        return solve(nonImportantApplications, 0, importantApplications, 0, 0, requiredMemory, 0);

    }

    private static long solve(
            List<Integer> nonImportant,
            int nonImportantStart,
            List<Integer> important,
            int importantStart,
            int memoryCollected,
            int memoryRequired,
            int lostConvenience
    ) {
        if (memoryCollected >= memoryRequired) {
            return lostConvenience;
        }
        if (nonImportantStart < nonImportant.size()
                && nonImportant.get(nonImportantStart) + memoryCollected >= memoryRequired) {
            return lostConvenience + 1;
        }
        if (nonImportantStart + 1 < nonImportant.size()
                && nonImportant.get(nonImportantStart) + nonImportant.get(nonImportantStart + 1) + memoryCollected >= memoryRequired) {
            return lostConvenience + 2;
        }
        if (importantStart + 1 < important.size()
                && important.get(importantStart) + memoryCollected >= memoryRequired) {
            return lostConvenience + 2;
        }

        if (nonImportantStart + 1 < nonImportant.size()) {
            if (importantStart < important.size()) {
                if (important.get(importantStart)
                        > nonImportant.get(nonImportantStart) + nonImportant.get(nonImportantStart + 1)) {
                    return solve(nonImportant, nonImportantStart, important, importantStart + 1, memoryCollected + important.get(importantStart), memoryRequired, lostConvenience + 2);
                }
            } else {
                return solve(nonImportant, nonImportantStart + 2, important, importantStart, memoryCollected + nonImportant.get(nonImportantStart) + nonImportant.get(nonImportantStart + 1), memoryRequired, lostConvenience + 2);
            }
        }

        if (importantStart  < important.size() && nonImportantStart < nonImportant.size()
                && important.get(importantStart) > nonImportant.get(nonImportantStart)) {
            return solve(nonImportant, nonImportantStart, important, importantStart, memoryCollected + important.get(importantStart), memoryRequired, lostConvenience + 2);
        }

        if (nonImportantStart < nonImportant.size()) {
            return solve(nonImportant, nonImportantStart + 1, important, importantStart, memoryCollected + nonImportant.get(nonImportantStart), memoryRequired, lostConvenience + 1);
        }
        if (importantStart < important.size()) {
            return solve(nonImportant, nonImportantStart, important, importantStart + 1, memoryCollected + important.get(importantStart), memoryRequired, lostConvenience + 2);
        }
        return -1;
    }

    public static long solve(
            List<Integer> nonImportantApplications,
            List<Integer> importantApplications,
            int requiredMemory,
            int memoryFreed,
            long convenienceLost
    ) {
        System.out.println("invoked");
        List<Integer> nonImportantCopy = new ArrayList<>(nonImportantApplications);
        List<Integer> importantCopy = new ArrayList<>(importantApplications);

        long result = -1;

        for (int i = 0; i < importantCopy.size(); i++) {
            Integer memory = importantCopy.remove(i);
            long maybeSolution = solve(nonImportantCopy, importantCopy, requiredMemory, memoryFreed + memory, convenienceLost + 2);
            if (maybeSolution != -1) {
                if (result == -1) {
                    result = maybeSolution;
                } else {
                    return Math.min(maybeSolution, result);
                }
            }

            for (int j = 0; j < nonImportantCopy.size(); j++) {
                int memory2 = nonImportantCopy.remove(j);
                long maybeSolution2 = solve(nonImportantCopy, importantCopy, requiredMemory, memoryFreed + memory2, convenienceLost + 1);
                if (maybeSolution2 != -1) {
                    if (result == -1) {
                        result = maybeSolution2;
                    } else {
                        return Math.min(maybeSolution2, result);
                    }
                }
                nonImportantCopy.add(j, memory2);
            }


            importantCopy.add(i, memory);
        }

        for (int j = 0; j < nonImportantCopy.size(); j++) {
            int memory2 = nonImportantCopy.remove(j);
            long maybeSolution2 = solve(nonImportantCopy, importantCopy, requiredMemory, memoryFreed + memory2, convenienceLost + 1);
            if (maybeSolution2 != -1) {
                if (result == -1) {
                    result = maybeSolution2;
                } else {
                    return Math.min(maybeSolution2, result);
                }
            }


            for (int i = 0; i < importantCopy.size(); i++) {
                Integer memory = importantCopy.remove(i);
                long maybeSolution = solve(nonImportantCopy, importantCopy, requiredMemory, memoryFreed + memory, convenienceLost + 2);
                if (maybeSolution != -1) {
                    if (result == -1) {
                        result = maybeSolution;
                    } else {
                        return Math.min(maybeSolution, result);
                    }
                }

                importantCopy.add(i, memory);
            }


            nonImportantCopy.add(j, memory2);
        }


        if (memoryFreed >= requiredMemory) {
            return convenienceLost;
        }
        return -1;
    }
}
