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.

//-------------------------------KING DONT LOOK DOWN---------------------------------------//

import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import java.awt.*;

public class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);
	static int[][] dirs = { { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 } };
	// static ArrayList<Integer>[] a;
	static ArrayList<Integer>[] g;
	static ArrayList<Integer>[] ra;
	// static int[] dp;
	static long[] fa;
	static int[] farr;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	static String s;
	// static long k = 0, n = 0, ans = 0;
	static long cnt;
	// static long[] dp;
	// static long[] p;
	// static long[] ans;
	// static Double[][] a = new Double[2][2];
	static Double[] x;
	static Double[] y;
	static long[] d;
	static int[][] par;
	static long[] v;
	static HashMap<Integer, Integer> map;
	// static ArrayList<Integer> p;
	static int time = 0;
	static int[] id;
	static TreeSet<Long> hm;
	static int[] ans;
	static boolean[] prime;

	public static void main(String[] args) throws IOException {

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));
		Reader scn = new Reader();

		int t = scn.nextInt();

		StringBuilder sb = new StringBuilder();

		z: while (t-- != 0) {

			int n = scn.nextInt();
			long m = scn.nextInt();

			long[] a = scn.nextLongArray(n);

			long[] b = scn.nextLongArray(n);

			long sum = 0;

			for (long i : a)
				sum += i;

			if (sum < m) {
				sb.append(-1);
				sb.append("\n");
				continue z;
			}

			ArrayList<Long> p = new ArrayList<>();// 1
			ArrayList<Long> q = new ArrayList<>();// 2

			for (int i = 0; i < n; i++) {

				if (b[i] == 1)
					p.add(a[i]);
				else
					q.add(a[i]);
			}

			Collections.sort(p, Collections.reverseOrder());
			Collections.sort(q, Collections.reverseOrder());

			long[] dp1 = new long[p.size()];
			long[] dp2 = new long[q.size()];

			if (dp1.length > 0)
				dp1[0] = p.get(0);

			if (dp2.length > 0)
				dp2[0] = q.get(0);

			for (int i = 1; i < p.size(); i++)
				dp1[i] = dp1[i - 1] + p.get(i);

			for (int i = 1; i < q.size(); i++)
				dp2[i] = dp2[i - 1] + q.get(i);

			long lo = 0, hi = 0, ans = 0;

			for (long i : b)
				hi += i;

			while (lo <= hi) {

				long mid = (lo + hi) / 2;

				if (f(dp1, dp2, mid, m)) {
					ans = mid;
					hi = mid - 1;
				}

				else
					lo = mid + 1;

			}

			sb.append(ans);
			sb.append("\n");

		}

		System.out.println(sb);

	}

	private static boolean f(long[] dp1, long[] dp2, long cnt, long m) {

		for (int i = 0; i <= Math.min(cnt, dp1.length  ); i++) {

			int rem = (int) ((cnt - i) / 2);

			rem = Math.min(rem, dp2.length);

			long val = m;

			if (rem - 1 >= 0)
				val -= dp2[rem - 1];

			if (i != 0)
				val -= dp1[i - 1];

			if (val <= 0)
				return true;
		}

		return false;
	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// if (!hm1.contains(p1))
	// return -1;
	// else if (!hm1.contains(p2))
	// return 1;
	// else
	// return 0;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b) {
	//
	// if (b < 0)
	// return 0;
	//
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int i, a, b;

		pair(int c, int d, int e) {

			i = c;
			a = d;
			b = e;
		}

		@Override
		public int compareTo(pair o) {

			return this.b - o.b;
		}

		@Override

		public String toString() {

			return i + " " + a + " " + b;
		}

		// @Override
		//
		// public int hashCode() {
		// return (int) (a * 17+);
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.a == p.a;
		// }
		//
		// @Override
		//
		// public String toString() {
		// return this.a + " ";
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

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

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}