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.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;



public class D {
    static int binarySearch(long arr[], long x) 
    { 
        int l = 0, r = arr.length - 1; 
        while (l <= r) { 
            int m = l + (r - l) / 2; 
            if (arr[m] == x) 
                return m; 
            if (arr[m] < x) 
                l = m + 1; 
            else
                r = m - 1; 
        } 
        if(l==arr.length)return -1;
        return l; 
    } 
    
    static void reverse(Integer a[]) 
    { 
    	int n=a.length;
        int i, k,t; 
        for (i = 0; i < n / 2; i++) { 
            t = a[i]; 
            a[i] = a[n - i - 1]; 
            a[n - i - 1] = t; 
        } 
  
    } 

	

	public static void main(String[] args) {
		
		FastScanner sc =new FastScanner(System.in);
		int t = sc.nextInt();
		for(;t>0;t--) {
			int n =sc.nextInt();
			long m =sc.nextLong();
            int av1[] = new int[n];
            int av2[] = new int[n];
            long sum = 0;
			for(int i = 0;i<n;i++) {
				av1[i]=sc.nextInt();
				sum+=av1[i];
			}

			int c1=0;
			int c2=0;
			for(int i = 0;i<n;i++) {
				av2[i]=sc.nextInt();
				if(av2[i]==1)c1++;
				else c2++;
			}
			if(sum<m) {
				System.out.println(-1);
				continue;
			}
			Integer a1Temp[]= new Integer[c1];
			Integer a2Temp[]= new Integer[c2];
			int p1Temp=0;
			int p2Temp=0;
			for(int i= 0 ;i<n;i++) {
				if(av2[i]==1)a1Temp[p1Temp++]=av1[i];
				else a2Temp[p2Temp++]=av1[i];
			}
			Arrays.sort(a1Temp);
			Arrays.sort(a2Temp);
            reverse(a1Temp);
            reverse(a2Temp);
			
			long a1[] = new long[c1];
			long a2[] = new long[c2];
			long ac1=0;
			long ac2=0;
			for(int i = 0;i<a1.length;i++) {
				a1[i]=a1Temp[i]+ac1;
				ac1=a1[i];
			}
			
			for(int i = 0;i<a2.length;i++) {
				a2[i]=a2Temp[i]+ac2;
				ac2=a2[i];
			}
//			System.out.println(Arrays.toString(a1Temp));
//			System.out.println(Arrays.toString(a2Temp));
//			System.out.println(Arrays.toString(a1));
//			System.out.println(Arrays.toString(a2));

			int pos = binarySearch(a2, m);
			int min = Integer.MAX_VALUE;
			
			if(pos!=-1)min=(pos+1)*2;
			for(int i = 0;i<a1.length;i++) {
				int j=-1;
				int temp=Integer.MAX_VALUE;;
				if(m-a1[i]>0) {
				    j= binarySearch(a2, m-a1[i]);
				    if(j==-1)continue;
					temp = (i+1)+(j+1)*2;
					//System.out.println(temp);
					if(temp<min)min=temp;
				}
				else if(m-a1[i]==0) {
					//System.out.println(m-a1[i]+" "+i);
					temp = (i+1);
					//System.out.println(temp);
					if(temp<min)min=temp;
				}
				
				//System.out.println(m-a1[i]+" "+i);
				temp = (i+1)+(j+1)*2;
				//System.out.println(temp);
				if(temp<min)min=temp;
			}
			
			System.out.println(min);
			
			
			
			
			
			
			
			
			
			
			
			
			

			
			
		}
		
		

	}
	static class element implements Comparable{
		int f;
		int c;
		int ind;
		double dif;
		public element(int f, int c, int ind) {
			this.f = f;
			this.c = c;
			this.ind = ind;
			dif=Math.ceil(f/(c*1.0));
		}
		@Override
		public int compareTo(Object o) {
			element e =(element)o;
			if(this.dif>e.dif)return -1;
			else if(this.dif<e.dif)return 1;
			else if(this.c<e.c) return -1;
			else if(this.c>e.c)return 1;
			else return 0;
			
		}
		@Override
		public String toString() {
			return "element [f=" + f + ", c=" + c + ", ind=" + ind + ", dif=" + dif + "]";
		}
		
		


	}
	
	
	
	
	
	
	
	
	static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                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());
        }
    }



}
