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 Solution {
      static class Reader{
          private final BufferedReader reader;
          private StringTokenizer tokenizer;
          Reader(InputStream input)
          {
              this.reader = new BufferedReader(new InputStreamReader(input));
              this.tokenizer = new StringTokenizer("");
          }
          public String next() throws IOException {
              while(!tokenizer.hasMoreTokens())
              {
                  tokenizer = new StringTokenizer(reader.readLine());
              }
              return tokenizer.nextToken();
          }
          public int nextInt() throws IOException
          {
              return Integer.parseInt(next());
          }
          public double nextDouble() throws IOException
          {
              return Double.parseDouble(next());
          }
          public long nextLong() throws IOException
          {
              return Long.parseLong(next());
          }
  
          public int[] nextIntArr(int n) throws IOException {
              int[] arr = new int[n];
              for(int i=0;i<n;i++)arr[i]=nextInt();
              return arr;
          }
          public long[] nextLongArr(int n)throws IOException {
              long[] arr = new long[n];
              for(int i=0;i<n;i++)arr[i]=nextLong();
              return arr;
          }
          public char[] nextCharArr(int n) throws IOException {
              char[] arr = new char[n];
              for(int i=0;i<n;i++)arr[i] = next().charAt(0);
              return arr;
          }
      }
      public static void main(String[] args) throws IOException {
          Reader scan = new Reader(System.in);
          StringBuffer sb = new StringBuffer();
          BufferedOutputStream bu = new BufferedOutputStream(System.out);
  
          int t = scan.nextInt();
          while (t-->0)
          {
              int n = scan.nextInt();
              long k = scan.nextLong();
              long[] inputArr = new long[n+1];
              long[] arr = new long[n+1];
              for(int i=1;i<=n;i++)inputArr[i] = scan.nextLong();
              Arrays.sort(inputArr);
              for(int i=1;i<=n;i++) {arr[i] += arr[i-1] + inputArr[i];}
              long ans = solve(arr, k);
              sb.append(ans+"\n");
          }
          bu.write((sb.toString()).getBytes());
          bu.flush();
      }
  
      private static long solve(long[] arr, long k) {
          long ans = Long.MAX_VALUE;
          for(long y=0;y<arr.length-1;y++)
          {
              long x = arr[1] - acurateFloor(k - arr[arr.length-1-(int)y] + arr[1], y+1);
              ans = Math.min(ans, y+Math.max(0, x));
          }
          return ans;
      }
  
      private static long acurateFloor(long l, long l1) {
          long ans = l/l1;
          while (ans*l1 > l)ans--;
          return ans;
      }
  }
  