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.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            DCleaningThePhone solver = new DCleaningThePhone();
            int testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(i, in, out);
            out.close();
        }
    }

    static class DCleaningThePhone {
        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt(), m = s.nextInt();
            long sum = 0;
//        ArrayList<Integer>[] mem = new ArrayList[2];
//        mem[0] = new ArrayList<>();
//        mem[1] = new ArrayList<>();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = s.nextInt();
                sum += a[i];
            }
            int[] b = new int[n], f = new int[2];
            for (int i = 0; i < n; i++) {
                b[i] = s.nextInt() - 1;
                f[b[i]]++;
            }
            if (sum < m) {
                w.println(-1);
                return;
            }
            long[][] mem = new long[2][];
            mem[0] = new long[f[0] + 1];
            mem[1] = new long[f[1] + 1];
            int[] ptr = new int[2];
            ptr[0] = ptr[1] = 1;
            for (int i = 0; i < n; i++) mem[b[i]][ptr[b[i]]++] = a[i];
            mem[0][0] = mem[1][0] = Integer.MAX_VALUE;
            func.sort(mem[0]);
            func.sort(mem[1]);
            for (int i = 0; i <= f[0] >> 1; i++) {
                long tm = mem[0][i];
                mem[0][i] = mem[0][f[0] - i];
                mem[0][f[0] - i] = tm;
            }
            for (int i = 0; i <= f[1] >> 1; i++) {
                long tm = mem[1][i];
                mem[1][i] = mem[1][f[1] - i];
                mem[1][f[1] - i] = tm;
            }
            mem[0][0] = mem[1][0] = 0;
            for (int i = 0; i < 2; i++)
                for (int j = 2; j <= f[i]; j++)
                    mem[i][j] += mem[i][j - 1];
            int res = f[0] + 2 * f[1];
//        if (n == 5 && m == 10) {
//            for (int i = 0; i <= f[0]; i++) w.print(mem[0][i] + " ");
//            w.println();
//            for (int i = 0; i <= f[1]; i++) w.print(mem[1][i] + " ");
//            w.println();
//        }
            for (int i = 0; i <= f[0]; i++) {
                long req = m - mem[0][i];
                int tot = func.bing(mem[1], 0, f[1], req);
                if (tot <= f[1]) res = Math.min(res, i + tot * 2);
            }
            w.println(res);
        }

    }

    static class func {
        public static int bing(long[] a, int l, int r, long val) {
            int mid;
            while (l <= r) {
                mid = l + r >> 1;
                if (a[mid] >= val) r = mid - 1;
                else l = mid + 1;
            }
            return ++r;
        }

        public static void sort(long[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            long[] res = new long[n];
            n--;
            for (s = 1; s <= n; s <<= 1) {
                for (l = 0; l < n; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n);
                    mid = Math.min(l + s - 1, n);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h)
                        res[k++] = arr[i] <= arr[j] ? arr[i++] : arr[j++];
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {

            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }

            return buf[curChar++];
        }

        public int nextInt() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();

                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public String next() {

            int c = read();

            while (isSpaceChar(c))
                c = read();

            StringBuilder res = new StringBuilder();

            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

