description: You are given an integer array a_1, a_2, ..., a_n and integer k.
  
  In one step you can 
  
    * either choose some index i and decrease a_i by one (make a_i = a_i - 1); 
    * or choose two indices i and j and set a_i equal to a_j (make a_i = a_j). 
  
  
  
  What is the minimum number of steps you need to make the sum of array ∑_{i=1}^{n}{a_i} ≤ k? (You are allowed to make values of array negative).
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
  
  The first line of each test case contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ k ≤ 10^{15}) — the size of array a and upper bound on its sum.
  
  The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the array itself.
  
  It's guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 10^5.
  
  Output
  
  For each test case, print one integer — the minimum number of steps to make ∑_{i=1}^{n}{a_i} ≤ k.
  
  Example
  
  Input
  
  
  4
  1 10
  20
  2 69
  6 9
  7 8
  1 2 1 3 1 2 1
  10 1
  1 2 3 1 2 6 1 6 8 10
  
  
  Output
  
  
  10
  0
  2
  7
  
  Note
  
  In the first test case, you should decrease a_1 10 times to get the sum lower or equal to k = 10.
  
  In the second test case, the sum of array a is already less or equal to 69, so you don't need to change it.
  
  In the third test case, you can, for example: 
  
    1. set a_4 = a_3 = 1; 
    2. decrease a_4 by one, and get a_4 = 0. 
  
  As a result, you'll get array [1, 2, 1, 0, 1, 2, 1] with sum less or equal to 8 in 1 + 1 = 2 steps.
  
  In the fourth test case, you can, for example: 
  
    1. choose a_7 and decrease in by one 3 times; you'll get a_7 = -2; 
    2. choose 4 elements a_6, a_8, a_9 and a_{10} and them equal to a_7 = -2. 
  
  As a result, you'll get array [1, 2, 3, 1, 2, -2, -2, -2, -2, -2] with sum less or equal to 1 in 3 + 4 = 7 steps.
solution: import java.io.*;
  import java.util.*;
  public class Main {
      public static void main(String args[])
      {
          FastReader input=new FastReader();
          PrintWriter out=new PrintWriter(System.out);
          int T=input.nextInt();
          while(T-->0)
          {
              int n=input.nextInt();
              long k=input.nextLong();
              ArrayList<Integer> list=new ArrayList<>();
              long sum=0;
              ArrayList<Long> sSum=new ArrayList<>();
              for(int i=0;i<n;i++)
              {
                  list.add(input.nextInt());
                  sSum.add(0l);
              }
              if(n==1)
              {
                  long op=Math.max(0,list.get(0)-k);
                  out.println(op);
              }
              else
              {
                  Collections.sort(list);
                  for(int i=n-1;i>=0;i--)
                  {
                      sum+=list.get(i);
                      sSum.set(i,sum);
                  }
                  long i=0,j=(long)1e18;
                  while(i<j)
                  {
                      long mid=(i+j)/2;
                      if(fun(sSum,k,mid,list.get(0),n,sum))
                      {
                          j=mid;
                      }
                      else
                      {
                          i=mid+1;
                      }
                  }
                  out.println(i);
              }
          }
          out.close();
      }
      public static boolean fun(ArrayList<Long> sSum,long k,long o,long min,int n,long sum)
      {
          if(o==0)
          {
              if(sum<=k) return true;
          }
          if(o==1)
          {
              if(sum-1<=k) return true;
          }
          int ind=1;
          if((long)n-o>1) ind=(int)(n-o);
          long rem=o-(n-ind);
          min-=rem;
          sum-=rem;
          while(ind<n)
          {
              long s=sSum.get(ind);
              long sum1=sum-s+((long)(n-ind)*min);
              if(sum1<=k) return true;
              ind++;
              min--;
              sum--;
          }
          return false;
      }
      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;
          }
      }
  }