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.*;
import java.util.*;

public class Main {
    static ArrayList<Integer> twos;
    public static int lowerBound(int target){
        int l = 0; int r = twos.size()-1;
        while(l < r){
            int mid = l + (r-l)/2;

            if(twos.get(mid) >= target) r = mid;
            else l = mid+1;
        }

        return r;
    }

    public static void main(String[] args) throws IOException, InterruptedException {
        int tc = sc.nextInt();
        while(tc --> 0) {
            int n = sc.nextInt(), m = sc.nextInt();
            int[] w = sc.nextIntArr(n);
            int[] c = sc.nextIntArr(n);
            ArrayList<Integer> ones = new ArrayList<>(); twos = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if(c[i] == 1) ones.add(w[i]);
                else twos.add(w[i]);
            }
            Collections.sort(ones, Collections.reverseOrder());
            Collections.sort(twos, Collections.reverseOrder());
            for (int i = 1; i < ones.size(); i++) {
                ones.set(i, ones.get(i-1) + ones.get(i));
            }
            for (int i = 1; i < twos.size(); i++) {
                twos.set(i, twos.get(i-1) + twos.get(i));
            }

//            pw.println(ones); pw.println(twos);

            int bestC = Integer.MAX_VALUE;
            for (int i = 0; i < twos.size(); i++) {
                if(twos.get(i) >= m){
                    bestC = Math.min(bestC, (i+1)*2);
                    break;
                }
            }
            
            for (int i = 0; i < ones.size(); i++) {
                int onesW = ones.get(i);
                if(onesW >= m) bestC = Math.min(bestC, i+1);
                else{
                    int idx = lowerBound(m-onesW);
                    if(idx == -1) continue;
                    int twosW = twos.get(idx);
                    int cost1 = i+1, cost2 = (idx+1)*2;
                    if(onesW + twosW >= m) bestC = Math.min(cost1+cost2, bestC);
                }
            }
            pw.println(bestC == Integer.MAX_VALUE ? -1 : bestC);
        }

        pw.close();
    }

    public static void pairSort(Pair[] arr) {
        ArrayList<Pair> l = new ArrayList<>();
        Collections.addAll(l, arr);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }
    public static void longSort(long[] arr) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : arr) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }
    public static void intSort(int[] arr) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : arr) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = l.get(i);
        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public int[] nextIntArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(next());
            }
            return arr;
        }

        public long[] nextLongArr(int n) throws IOException {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = Long.parseLong(next());
            }
            return arr;
        }

    }
    static class Pair implements Comparable<Pair>{
        long first; long second;
        public Pair(long first, long second){
            this.first = first; this.second = second;
        }

        @Override
        public int compareTo(Pair p2) {
            if(second == p2.second) return (int) (p2.first - first);
            else return (int) (second - p2.second);
        }

        @Override
        public String toString() { return "("+ first + "," + second + ')'; }
    }
    static class Triple implements Comparable<Triple> {
        double x, y, z, sum;

        Triple(double a, double b, double c) { x = a; y = b; z = c; sum = x + y + z; }


        public int compareTo(Triple t)
        {
            if(Math.abs(sum - t.sum) < 1e-9) return x > t.x ? 1 : -1;
            return sum > t.sum ? 1 : -1;
        }
        public String toString()
        {
            return x + " " + y  + " " + z;
        }
    }

    static PrintWriter pw = new PrintWriter(System.out);
    static Scanner sc = new Scanner(System.in);
    static Random random = new Random();
    static final long MOD = 1073741824;
}