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 a2oj {

    static FastReader sc;
    static PrintWriter out;
    static int mod = 1000000007;

    public static void main(String[] args) {
        sc = new FastReader();
        out = new PrintWriter(System.out);
        solve(sc, out);
        out.flush();
        out.close();
    }

    static void solve(FastReader sc, PrintWriter out) {
        int t = sc.nextInt();
        StringBuffer ans = new StringBuffer("");
        while (t-- > 0) {
            int n = sc.nextInt();
            long m = sc.nextLong();
            long[] a = new long[n], b = new long[n];
            ArrayList<Pair> arr = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextLong();
            }
            for (int i = 0; i < n; i++) {
                b[i] = sc.nextLong();
            }
            for (int i = 0; i < n; i++) {
                arr.add(new Pair(a[i], b[i]));
            }
            Collections.sort(arr);
            long sum = 0, sum1 = 0;
            for (Pair e : arr) {
                if (sum >= m)
                    break;
                sum += e.x;
                sum1 += e.y;
            }
            Collections.sort(arr, (a1, b1) -> {
                if (a1.y == b1.y)
                    return (int) (b1.x - a1.x);
                return (int) (a1.y - b1.y);
            });
            long sum2 = 0, sum3 = 0;
            for (Pair e : arr) {
                if (sum2 >= m)
                    break;
                sum2 += e.x;
                sum3 += e.y;
            }
            if (sum < m && sum2 < m) {
                ans.append("-1\n");
            } else {
                if (sum3 > 0 && sum1 > 0)
                    ans.append(Math.min(sum1, sum3) + "\n");
                else if (sum3 > 0)
                    ans.append(sum3 + "\n");
                else if (sum1 > 0)
                    ans.append(sum1 + "\n");
            }
        }
        out.println(ans);
    }

    public static boolean isPowerTwo(long n) {
        return (n & n - 1) == 0;
    }

    static void sieve(boolean[] prime, int n) { // Sieve Of Eratosthenes
        for (int i = 1; i <= n; i++) {
            prime[i] = true;
        }
        for (int i = 2; i * i <= n; i++) {
            if (prime[i]) {
                for (int j = 2; i * j <= n; j++) {
                    prime[i * j] = false;
                }
            }
        }
    }

    static void fillGraph(ArrayList<ArrayList<Integer>> adj, FastReader sc) {
        int n = sc.nextInt(), m = sc.nextInt();
        for (int i = 0; i < n + 1; i++) {
            adj.add(new ArrayList<Integer>());
        }
        for (int i = 1; i <= m; i++) {
            int x = sc.nextInt(), y = sc.nextInt();
            adj.get(x).add(y);
            adj.get(y).add(x);
        }
    }

    static void dfs(ArrayList<ArrayList<Integer>> adj, boolean[] visited, int v, PrintWriter out) {
        visited[v] = true;
        out.print(v + " ");
        for (Integer i : adj.get(v)) {
            if (!visited[i])
                dfs(adj, visited, i, out);
        }
    }

    static void bfs(ArrayList<ArrayList<Integer>> adj, int V, int s, PrintWriter out) {
        boolean[] visited = new boolean[V];
        Queue<Integer> q = new LinkedList<>();
        visited[s] = true;
        q.add(s);
        while (!q.isEmpty()) {
            s = q.poll();
            out.print(s + " ");
            for (Integer i : adj.get(s)) {
                if (!visited[i]) {
                    visited[i] = true;
                    q.add(i);
                }
            }
        }
    }

    int fib(int n) { // n-th Fibonacci Number
        int a = 0, b = 1, c, i;
        if (n == 0)
            return a;
        for (i = 2; i <= n; i++) {
            c = a + b;
            a = b;
            b = c;
        }
        return b;
    }

    static long nCr(int n, int r) { // Combinations
        if (n < r)
            return 0;
        if (r > n - r) { // because nCr(n, r) == nCr(n, n - r)
            r = n - r;
        }
        long ans = 1L;
        for (int i = 0; i < r; i++) {
            ans *= (n - i);
            ans /= (i + 1);
        }
        return ans;
    }

    static long catalan(int n) { // n-th Catalan Number
        long c = nCr(2 * n, n);
        return c / (n + 1);
    }

    static class Pair implements Comparable<Pair> { // Pair Class
        long x;
        long y;

        Pair(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            if (this.x == o.x) {
                return (int) (this.y - o.x);
            }
            return (int) (o.x - this.x);
        }
    }

    static class Trip<E, T, Z> { // Triplet Class
        E x;
        T y;
        Z z;

        Trip(E x, T y, Z z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Trip<E, T, Z> o) {
            if (o instanceof Trip) {
                Trip<E, T, Z> t = o;
                return t.x == x && t.y == y && t.z == z;
            }
            return false;
        }

        public int hashCode() {
            return Integer.valueOf((int) x).hashCode() * 62 + Integer.valueOf((int) y).hashCode() * 31
                    + Integer.valueOf((int) z).hashCode();
        }
    }

    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;
        }
    }

}