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.PrintWriter;
  import java.util.Arrays;
  import java.util.InputMismatchException;
  import java.io.IOException;
  import java.util.Random;
  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);
          PrintWriter out = new PrintWriter(outputStream);
          CPrisvoitIliUmenshit solver = new CPrisvoitIliUmenshit();
          int testCount = Integer.parseInt(in.next());
          for (int i = 1; i <= testCount; i++)
              solver.solve(i, in, out);
          out.close();
      }
  
      static class CPrisvoitIliUmenshit {
          long MAX = (long) 1e10 + 10;
  
          public void solve(int testNumber, InputReader in, PrintWriter out) {
              int n = in.nextInt();
              long k = in.nextLong();
              long[] a = new long[n];
  
              for (int i = 0; i < n; i++) {
                  a[i] = in.nextLong();
              }
              CPrisvoitIliUmenshit.ArrayUtils.sort(a);
  
              long[] cum = new long[n];
              cum[0] = a[0];
              for (int i = 1; i < n; i++) {
                  cum[i] = cum[i - 1] + a[i];
              }
  
              long all = cum[n - 1];
              long min = a[0];
  
              long mmin = Integer.MAX_VALUE;
  
              for (int i = 1; i <= n; i++) {
                  long t1 = 0;
                  long t2 = MAX * 2;
                  while (t1 < t2) {
                      long mid = (t1 + t2) / 2;
                      long curmin = min - mid;
                      long was = all - cum[i - 1];
                      long tobe = curmin * (n - i);
                      long overall = all - min + curmin - was + tobe;
                      if (overall > k) {
                          t1 = mid + 1;
                      } else {
                          t2 = mid;
                      }
                  }
                  mmin = Math.min(mmin, n - i + t1);
              }
              out.println(mmin);
          }
  
          public static class ArrayUtils {
              static final long seed = System.nanoTime();
              static final Random rand = new Random(seed);
  
              public static void sort(long[] a) {
                  shuffle(a);
                  Arrays.sort(a);
              }
  
              public static void shuffle(long[] a) {
                  for (int i = 0; i < a.length; i++) {
                      int j = rand.nextInt(i + 1);
                      long t = a[i];
                      a[i] = a[j];
                      a[j] = t;
                  }
              }
  
          }
  
      }
  
      static class InputReader {
          private static final int BUFFER_LENGTH = 1 << 10;
          private InputStream stream;
          private byte[] buf = new byte[BUFFER_LENGTH];
          private int curChar;
          private int numChars;
  
          public InputReader(InputStream stream) {
              this.stream = stream;
          }
  
          private int nextC() {
              if (numChars == -1) {
                  throw new InputMismatchException();
              }
              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
                  if (numChars <= 0)
                      return -1;
              }
              return buf[curChar++];
          }
  
          public String next() {
              int c = nextC();
              while (isSpaceChar(c)) {
                  c = nextC();
              }
              StringBuilder res = new StringBuilder();
              do {
                  res.append((char) c);
                  c = nextC();
              } while (!isSpaceChar(c));
              return res.toString();
          }
  
          public int nextInt() {
              int c = skipWhileSpace();
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = nextC();
              }
              int res = 0;
              do {
                  if (c < '0' || c > '9') {
                      throw new InputMismatchException();
                  }
                  res *= 10;
                  res += c - '0';
                  c = nextC();
              } while (!isSpaceChar(c));
              return res * sgn;
          }
  
          public long nextLong() {
              int c = skipWhileSpace();
              long sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = nextC();
              }
              long res = 0;
              do {
                  if (c < '0' || c > '9') {
                      throw new InputMismatchException();
                  }
                  res *= 10;
                  res += c - '0';
                  c = nextC();
              } while (!isSpaceChar(c));
              return res * sgn;
          }
  
          public int skipWhileSpace() {
              int c = nextC();
              while (isSpaceChar(c)) {
                  c = nextC();
              }
              return c;
          }
  
          public boolean isSpaceChar(int c) {
              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }
  
      }
  }
  
  