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.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.OutputStream;
  import java.io.PrintWriter;
  import java.util.Arrays;
  import java.io.BufferedWriter;
  import java.io.IOException;
  import java.util.Random;
  import java.io.InputStreamReader;
  import java.util.StringTokenizer;
  import java.io.Writer;
  import java.io.OutputStreamWriter;
  import java.io.BufferedReader;
  import java.io.InputStream;
  
  /**
   * Built using CHelper plug-in
   * Actual solution is at the top
   */
  public class Main {
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          OutputWriter out = new OutputWriter(outputStream);
          CSetOrDecrease solver = new CSetOrDecrease();
          int testCount = Integer.parseInt(in.next());
          for (int i = 1; i <= testCount; i++)
              solver.solve(i, in, out);
          out.close();
      }
  
      static class CSetOrDecrease {
          int n;
          long k;
          int[] arr;
          long[] pref;
  
          public void solve(int testNumber, InputReader in, OutputWriter out) {
              n = in.nextInt();
              k = in.nextLong();
              arr = in.nextIntArray(n);
              sort(arr);
              pref = new long[n];
              pref[0] = arr[0];
              long sum = arr[0];
              for (int i = 1; i < n; i++) {
                  pref[i] = pref[i - 1] + arr[i];
                  sum += arr[i];
              }
              if (sum <= k) {
                  out.println(0);
                  return;
              }
              if (sum == k + 1) {
                  out.println(1);
                  return;
              }
              if (n == 1) {
                  out.println(sum - k);
                  return;
              }
              long ans = Long.MAX_VALUE;
              for (int i = n - 1; i >= 0; i--) {
                  long lo = arr[0] - (sum - k) / (n - i + 1) - 2;
  //            out.println(lo);
                  long hi = arr[0];
                  long val = 0;
                  while (lo <= hi) {
                      long mid = (lo + hi) / 2;
                      if (check(mid, i - 1)) {
                          val = mid;
                          lo = mid + 1;
                      } else {
                          hi = mid - 1;
                      }
                  }
                  ans = Math.min(ans, (n >= 2 ? n - i : 0) + arr[0] - val);
              }
              out.println(ans);
          }
  
          boolean check(long mid, int l) {
              long val = (l < 0 ? ((long) n * mid) : (pref[l] - arr[0] + (long) (n - l) * mid));
              return val <= k;
          }
  
          void sort(int[] a) {
              int n = a.length;
              Random r = new Random();
              for (int i = 0; i < a.length; i++) {
                  int oi = r.nextInt(n), temp = a[i];
                  a[i] = a[oi];
                  a[oi] = temp;
              }
              Arrays.sort(a);
          }
  
      }
  
      static class InputReader {
          BufferedReader reader;
          StringTokenizer tokenizer;
  
          public InputReader(InputStream stream) {
              reader = new BufferedReader(new InputStreamReader(stream), 32768);
              tokenizer = null;
          }
  
          public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public int[] nextIntArray(int n) {
              int[] array = new int[n];
              for (int i = 0; i < n; ++i) array[i] = nextInt();
              return array;
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
      }
  
      static class OutputWriter {
          private final PrintWriter writer;
  
          public OutputWriter(OutputStream outputStream) {
              writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
          }
  
          public OutputWriter(Writer writer) {
              this.writer = new PrintWriter(writer);
          }
  
          public void close() {
              writer.close();
          }
  
          public void println(long i) {
              writer.println(i);
          }
  
          public void println(int i) {
              writer.println(i);
          }
  
      }
  }
  
  