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 {
      static Long[] array;
      public static long check(int location, long reduction) {
          long numSteps = array.length - location;
          long normalReduction = array[location];
          if (normalReduction >= reduction) {
              return numSteps;
          } else {
              long targetReduce = reduction - normalReduction;
              long reduceQuantity = numSteps + 1;
              if (targetReduce % reduceQuantity == 0) {
                  return numSteps + targetReduce/reduceQuantity;
              } else {
                  return numSteps + targetReduce/reduceQuantity + 1;
              }
          }
      }
      public static void main(String[] args) throws IOException {
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
          int numCases = Integer.parseInt(br.readLine());
          for (int i = 0; i < numCases; i++) {
              StringTokenizer st = new StringTokenizer(br.readLine());
              int size = Integer.parseInt(st.nextToken());
              long upperBound = Long.parseLong(st.nextToken());
              array = new Long[size];
              long sum = 0;
              st = new StringTokenizer(br.readLine());
              for (int j = 0; j < size; j++) {
                  Long num = Long.parseLong(st.nextToken());
                  sum += num;
                  array[j] = num;
              }
              Arrays.sort(array);
              long minimum = array[0];
              long reduction = sum - upperBound;
  
              if (sum <= upperBound) {
                  pw.println(0);
              } else if (size == 1) {
                  pw.println(sum - upperBound);
              } else {
                  long total = 0;
                  for (int j = size - 1; j >= 0; j--) {
                      long diff = array[j] - minimum;
                      total += diff;
                      array[j] = total;
                  }
  //                int lo = 1;
  //                int hi = size - 1;
  //                while (lo < hi) {
  //                    int mid = lo + (hi - lo) / 2;
  //                    if (check(mid, reduction) < check(mid + 1, reduction)) {
  //                        hi = mid;
  //                    } else {
  //                        lo = mid + 1;
  //                    }
  //                }
  //                pw.println(Math.min(check(lo, reduction), reduction));
                  long ret = reduction;
                  for (int j = 1; j < size; j++) {
                      ret = Math.min(ret, check(j, reduction));
                  }
                  pw.println(ret);
              }
          }
          br.close();
          pw.close();
      }
  }