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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class CodeForces extends Functions {
    static Scanner sc = new Scanner();
    public static void  solve() {
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] arr = sc.setIntArray(n);
        int[] brr = sc.setIntArray(n);
        List<Integer> imp = new ArrayList<>();
        List<Integer> reg = new ArrayList<>();
        sort(arr,false);
        for(int i=0;i<n;i++){
            if(brr[i]==1)reg.add(arr[i]);
            else imp.add(arr[i]);
        }

        long[] impPre = new long[imp.size()];
        if(impPre.length>0)impPre[0] = imp.get(0);
        for(int i=1;i<impPre.length;i++)
            impPre[i] = imp.get(i) + impPre[i-1];
        long[] regPre = new long[reg.size()];
        if(regPre.length>0)regPre[0] =reg.get(0);
        for(int i=1;i<regPre.length;i++)
            regPre[i] = reg.get(i) + regPre[i-1];
        int ans = Integer.MAX_VALUE;
        for(int i=0;i<impPre.length;i++){
            int curr = 2 * (i+1);
            int[] tt = bs(k-impPre[i],regPre);
            // System.out.println(curr+" "+ Arrays.toString(tt));
            if(tt[0]==1)
                ans  = Math.min(ans,curr+tt[1]);
            if(impPre[i]>=k)
                ans  = Math.min(ans,curr);
        }
        int[] tt = bs(k,regPre);
        if(tt[0]==1)ans  = Math.min(ans,tt[1]);
        if(ans == Integer.MAX_VALUE)System.out.println(-1);
        else System.out.println(ans);

    }
    private static int[] bs(long ele,long[] arr){
       if(ele<=0)return new int[]{1,0};
       int l = 0;
       int r = arr.length-1;
       if(r>=0 && ele<=arr[0])return new int[]{1,1};
       while(l<=r){
           int mid = (r-l)/2 + l;
           if(mid>=1 && arr[mid]>=ele && arr[mid-1]<ele)
               return new int[]{1,mid+1};
           if(arr[mid]>=ele)
               r = mid-1;
           else l = mid+1;
       }
       return new int[]{0,0};
   }

    public static void main(String[] args) {
       int testCase = 1;
       testCase= sc.nextInt();
        while (testCase-->0){
            solve();
        }
        long end = System.currentTimeMillis();
//        System.out.println("time took in ms : "+(end-start));
    }


}
class Functions {
    public static int mod = (int)1e9+7;
    public static int INT_MAX = Integer.MAX_VALUE;
    public static int INT_MIN = Integer.MIN_VALUE;
    public static long LONG_MAX = Long.MAX_VALUE;
    public static long LONG_MIN = Long.MIN_VALUE;
    public static double DOUBLE_MAX = Double.MAX_VALUE;
    public static double DOUBLE_MIN = Double.MIN_VALUE;

    public static void sort(int[] a,boolean isAscending){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp,isAscending);
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }
    public static void sort(List T,boolean isAscending){
        if(isAscending)
            Collections.sort(T);
        else Collections.sort(T,Collections.reverseOrder());
    }
    public static long factorial(int n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact=  (fact*i)%mod;
        return fact;
    }

    public  static int ncr(int n, int r){
        // time O(n+r)
        if (r > n)
            return 0;
        long[] inv = new long[r + 1];
        inv[1] = 1;
        // Getting the modular inversion
        // for all the numbers
        // from 2 to r with respect to m
        for (int i = 2; i <= r; i++) {
            inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
        }
        int ans = 1;
        // for 1/(r!) part
        for (int i = 2; i <= r; i++) {
            ans = (int) (((ans % mod) * (inv[i] % mod)) % mod);
        }
           // for (n)*(n-1)*(n-2)*...*(n-r+1) part
        for (int i = n; i >= (n - r + 1); i--) {
            ans = (int) (((ans % mod) * (i % mod)) % mod);
        }
        return ans;
    }

    public static void reverseArray(int[] a){
        int left = 0;
        int right = a.length-1;
        while (left<right){
            int temp =a[left];
            a[left] = a[right];
            a[right] = temp;
            left++;
            right--;
        }
    }
    public static long isPrime(int n){
        for(long i=2;i*i<=n;i++)
            if(n%i==0)return i;
        return -1;
    }
}

class Scanner {
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer st = new StringTokenizer("");
    public String next(){
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            }catch (IOException e){
                e.printStackTrace();
            }
        return st.nextToken();

    }
    public int nextInt(){return Integer.parseInt(next());}
    public long nextLong(){return Long.parseLong(next());}
    public double nextDouble(){return Double.parseDouble(next());}
    public int[] setIntArray(int n){
        int[] arr =new int[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public Integer[] setIntegerArray(int n){
        Integer[] arr =new Integer[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public long[] setlongArray(int n){
        long[] arr =new long[n];
        for(int i=0;i<n;i++)arr[i] = nextLong();
        return arr;
    }
    public int[][] set2DIntegerMatrix(int row,int col){
        int[][] arr = new int[row][col];
        for(int i=0;i<row;i++)
            for(int j= 0;j<col;j++)
                arr[i][j] = nextInt();
        return arr;
    }
}
