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.util.*;
import java.io.*;

public class Solution {
    public static void main(String[] args){
        int t;
        int n;
        long m;
        ArrayList<Long> memSize = new ArrayList<Long>();
        ArrayList<Integer> cps = new ArrayList<Integer>();
        long totalMemory = 0L;
        ArrayList<Integer> ans = new ArrayList<Integer>();
        ArrayList<App> apps = new ArrayList<App>();
        Scanner s = new Scanner(System.in);
        t=s.nextInt();
        for(int i=0; i<t; i++){
            n = s.nextInt();
            m = s.nextLong();
            memSize.clear();
            cps.clear();
            apps.clear();
            totalMemory = 0L;
            for(int j=0; j<n; j++){
                Long tempMem = s.nextLong();
                memSize.add(tempMem);
                totalMemory += tempMem;
            }
            for(int j=0; j<n; j++){
                int tempcp = s.nextInt();
                cps.add(tempcp);
                apps.add(new App(tempcp, memSize.get(j)));
            }
            ans.add(solve(totalMemory,n,m,memSize,cps, apps));
        }
        for(int i=0; i<t; i++){
            System.out.println(ans.get(i));
        }
    }

    public static class App{
        int cp;
        long mem;
        public App(int c, long m){
            this.cp = c;
            this.mem = m;
        }
    }

    public static int solve(long totalMemory, int n, long m, ArrayList<Long> memSize, ArrayList<Integer> cps, ArrayList<App> apps){
        int totalCP = 0;
        int cpLoss = 0;
        long memFree = 0L;
        int appsDel = 0;
        int minCPLoss = Integer.MAX_VALUE;
        apps.sort(new Sortbymem());
        if(totalMemory < m){
            return -1;
        }else{
            for(int i=0; i<n; i++){
                totalCP+=cps.get(i);
            }
            if(totalMemory==m){
                return totalCP;
            }else{
                // for(int i=0; i<apps.size(); i++){
                //     System.out.print(apps.get(i).cp + " , " + apps.get(i).mem + " | ");
                // }
                // System.out.println();
                int x = 0;
                int y = 0 ;
                boolean flag = true;
            
                while(true){

                    while(memFree<m && x<n){
                        // System.out.println("x: "+x);
                        memFree+=apps.get(x).mem;
                        cpLoss+=apps.get(x).cp;
                        // System.out.println("cpLoss "+cpLoss+", memFree "+memFree);
                        x++;
                    }

                    minCPLoss = Math.min(minCPLoss,cpLoss);
                    // System.out.println("Min cpLoss" + minCPLoss);

                    while(memFree>m){
                        memFree-=apps.get(y).mem;
                        cpLoss-=apps.get(y).cp;
                    }

                    if(memFree>=m){
                        minCPLoss = Math.min(minCPLoss,cpLoss);
                        // System.out.println("Min cpLoss" + minCPLoss);
                    }

                    // System.out.println("Min cpLoss" + minCPLoss);

                    // System.out.println("x is "+x);
                    // System.out.println("n is "+n);
                    if(memFree==m || x==n){
                        // System.out.println("Breaking...");
                        break;
                    }

                }
                return minCPLoss;
            }
        }

    }

    static class Sortbymem implements Comparator<App>
{
    // Used for sorting in ascending order of
    // roll number
    public int compare(App a, App b)
    {
        if((a.cp-b.cp)==0 && (a.mem!=b.mem)){
            return Integer.parseInt(String.valueOf((b.mem - a.mem)/Math.abs(a.mem - b.mem)));
        }else{
            return (a.cp-b.cp);
        }
    }
}
}
