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 final FastReader FR = new FastReader();
  static final PrintWriter PW = new PrintWriter(new OutputStreamWriter(System.out));
 
  public static void main(String[] args) {
    StringBuilder solution = new StringBuilder();
    int tests = 1;
    tests = FR.nextInt();
    for (int t = 0; t < tests; ++t) {
      int appCount = FR.nextInt();
      int memReqd = FR.nextInt();
      int[] memUsed = new int[appCount];
      for (int i = 0; i < appCount; i += 1) {
        memUsed[i] = FR.nextInt();
      }
      int[] convPts = new int[appCount];
      for (int i = 0; i < appCount; i += 1) {
        convPts[i] = FR.nextInt();
      }
      int ConvPtsLost = computeConvPtsLoss(memReqd, memUsed, convPts);
      solution.append(ConvPtsLost + "\n");
    }
		PW.print(solution.toString());
    PW.close();
  }

  static int computeConvPtsLoss(int memReqd, int[] memUsed, int[] convPts) {
    List<Integer> memSingleCP = new ArrayList<Integer>(memUsed.length>>1);
    List<Integer> memDoubleCP = new ArrayList<Integer>(memUsed.length>>1);
    for (int i = 0; i < memUsed.length; i += 1) {
      if (convPts[i] == 1) {
        memSingleCP.add(memUsed[i]);
      } else {
        memDoubleCP.add(memUsed[i]);
      }
    }
    Collections.sort(memSingleCP, Collections.reverseOrder());
    Collections.sort(memDoubleCP, Collections.reverseOrder());
    int singleSize = memSingleCP.size();
    int doubleSize = memDoubleCP.size();

    int singlePtr, doublePtr;
    singlePtr = doublePtr = 0;
    int memFreed, evenConvPtsLost;
    memFreed = evenConvPtsLost = 0;
    
    // Assuming even number of singleCP elements consumed
    while (memFreed < memReqd) {
      evenConvPtsLost += 2;
      int singlesLeft = singleSize - singlePtr;
      int doublesLeft = doubleSize - doublePtr;
      if (singlesLeft > 1) {
        int singleConsider = memSingleCP.get(singlePtr) + memSingleCP.get(singlePtr+1);
        int doubleConsider = doublesLeft > 0 ? memDoubleCP.get(doublePtr) : -1;
        if (singleConsider > doubleConsider) {
          memFreed += singleConsider;
          singlePtr += 2;
        } else {
          memFreed += doubleConsider;
          doublePtr += 1;
        }
      } else if (doublesLeft > 0) {
        memFreed += memDoubleCP.get(doublePtr++);
      } else {
        evenConvPtsLost = -1;
        break;
      }
    }
    if (memFreed < memReqd) evenConvPtsLost = -1;
    if (memSingleCP.size() == 0) return evenConvPtsLost;

    // Assuming odd number of singleCP elements consumed
    singlePtr = doublePtr = 0;
    memFreed = memSingleCP.get(singlePtr++);
    int oddConvPtsLost = 1;
    while (memFreed < memReqd) {
      oddConvPtsLost += 2;
      int singlesLeft = singleSize - singlePtr;
      int doublesLeft = doubleSize - doublePtr;
      if (singlesLeft > 1) {
        int singleConsider = memSingleCP.get(singlePtr) + memSingleCP.get(singlePtr+1);
        int doubleConsider = doublesLeft > 0 ? memDoubleCP.get(doublePtr) : -1;
        if (singleConsider > doubleConsider) {
          memFreed += singleConsider;
          singlePtr += 2;
        } else {
          memFreed += doubleConsider;
          doublePtr += 1;
        }
      } else if (doublesLeft > 0) {
        memFreed += memDoubleCP.get(doublePtr++);
      } else {
        oddConvPtsLost = -1;
        break;
      }
    }
    if (memFreed < memReqd) oddConvPtsLost = -1;
    
    if (oddConvPtsLost == -1 && evenConvPtsLost == -1) return -1;
    if (oddConvPtsLost == -1) return evenConvPtsLost;
    if (evenConvPtsLost == -1) return oddConvPtsLost;
    return Math.min(evenConvPtsLost, oddConvPtsLost);
  }
 
  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;
    }
  }
}