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.Closeable;
  import java.io.DataInputStream;
  import java.io.FileInputStream;
  import java.io.IOException;
  import java.util.Arrays;
  import java.util.Comparator;
  import java.util.function.Function;
  import java.util.function.IntFunction;
  import java.util.stream.Collectors;
  
  public class C {
      public static void main(String[] args) throws IOException {
          FastScanner scanner = new FastScanner();
          int t = scanner.nextInt();
          while (t-- > 0) {
              int[] a = new int[scanner.nextInt()];
              long k = scanner.nextLong();
              long sum = 0;
              for (int i = 0; i < a.length; i++) {
                  a[i] = scanner.nextInt();
                  sum += a[i];
              }
              a = Arrays.stream(a).boxed().sorted(Comparator.reverseOrder()).mapToInt(i -> i).toArray();
              int min = a[a.length - 1];
              long[] b = new long[a.length];
              for (int i = 0; i < a.length - 1; i++) b[i + 1] = a[i] - min;
              for (int i = 1; i < b.length; i++) b[i] += b[i - 1];
  
              long minOps = Long.MAX_VALUE;
              for (int replaces = 0; replaces < b.length; replaces++) {
                  long reduces = (long) Math.ceil((sum - b[replaces] - k) / (double)(replaces + 1));
                  reduces = Math.max(reduces, 0);
                  minOps = Math.min(minOps, reduces + replaces);
              }
              System.out.println(minOps);
  //            int reduces = 0;
  //            while (sum - b[b.length - 1] - reduces * a.length > k) reduces++;
  //            int replaces = b.length - 1;
  //            while (replaces > 0 && sum - b[replaces - 1] - reduces * (1 + replaces - 1) <= k) replaces--;
  
  //            System.out.println(reduces + replaces);
          }
      }
  
      /**
       * Credits: https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
       */
      private static class FastScanner implements Closeable {
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
  
          public FastScanner() {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public FastScanner(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[64];
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n' || c == '\r') {
                      if (cnt != 0) {
                          break;
                      } else {
                          continue;
                      }
                  }
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          public String next() throws IOException {
              return next(32);
          }
  
          public String next(int len) throws IOException {
              byte[] buf = new byte[len];
              int ptr = 0;
              byte c = read();
              while (c <= ' ') c = read();
              do {
                  if (ptr == buf.length) {
                      buf = Arrays.copyOf(buf, buf.length << 1);
                  }
                  buf[ptr++] = c;
              } while ((c = read()) > ' ');
              if (buf.length == ptr) return new String(buf);
              return new String(Arrays.copyOf(buf, ptr));
          }
  
          public int nextInt() throws IOException {
              int ret = 0;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg) return -ret;
              return ret;
          }
  
          public long nextLong() throws IOException {
              long ret = 0;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (neg) return -ret;
              return ret;
          }
  
          public double nextDouble() throws IOException {
              double ret = 0, div = 1;
              byte c = read();
              while (c <= ' ') c = read();
              boolean neg = (c == '-');
              if (neg) c = read();
              do {
                  ret = ret * 10 + c - '0';
              } while ((c = read()) >= '0' && c <= '9');
              if (c == '.') {
                  while ((c = read()) >= '0' && c <= '9') {
                      ret += (c - '0') / (div *= 10);
                  }
              }
              if (neg) return -ret;
              return ret;
          }
  
          private void fillBuffer() throws IOException {
              bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
              if (bytesRead == -1) buffer[0] = -1;
          }
  
          private byte read() throws IOException {
              if (bufferPointer == bytesRead) fillBuffer();
              return buffer[bufferPointer++];
          }
  
          @Override
          public void close() throws IOException {
              if (din == null) return;
              din.close();
          }
      }
  }
  