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 TaskC {
  
      public static void main(String[] arg) throws FileNotFoundException {
          final FastScanner in = new FastScanner(System.in);
          final PrintWriter out = new PrintWriter(System.out);
          final int T = in.nextInt();
          for (int t = 1; t <= T; t++) {
              final int n = in.nextInt();
              final long k = in.nextLong();
              final long[] a = in.readLongArr(n);
              Solution sol = new Solution(n, k, a);
              out.println(sol.sol());
          }
          out.flush();
          out.close();
          in.close();
      }
  
      public static class Solution {
          final long[] a;
          final long k;
          final int n;
  
          public Solution(int n, long k, long[] a) {
              this.a = a;
              this.k = k;
              this.n = n;
          }
  
          public long sol() {
              sort(a);
              long sum = 0;
              for (int i = 0; i < n; i++) {
                  sum += a[i];
              }
              if (sum <= k) {
                  return 0;
              }
              if (n == 1) {
                  return a[0] - k;
              }
              long prefix = sum - a[0];
              long a0 = k - prefix;
              long min = a[0] - a0;
              //k >= prefix+a0
              //a[0]>=a[0] k-sum
              for (int i = 1; i <= n - 1; i++) {
                  prefix -= a[n - i];
                  //k>=2*a0+prefix
                  a0 = Math.min(a[0], (k - prefix) / (i + 1));
                  if (a0 * (i + 1) + prefix > k) {
                      a0--;
                  }
                  min = Math.min(a[0] - a0 + i, min);
              }
              return min;
          }
      }
  
      public static void sort(long[] a) {
          Random r1 = new Random();
          for (int i = 0; i < a.length; i++) {
              int r = r1.nextInt(a.length);
              long temp = a[i];
              a[i] = a[r];
              a[r] = temp;
          }
          Arrays.sort(a);
      }
  
  
      private 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());
          }
  
          int[] readIntArr(int n) {
              int[] result = new int[n];
              for (int i = 0; i < n; i++) {
                  result[i] = Integer.parseInt(next());
              }
              return result;
          }
  
          long[] readLongArr(int n) {
              long[] result = new long[n];
              for (int i = 0; i < n; i++) {
                  result[i] = Long.parseLong(next());
              }
              return result;
          }
  
          void close() {
              try {
                  br.close();
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
      }
  
  }
  