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.math.BigInteger;
  import java.util.*;
  
  import javax.swing.text.AbstractDocument.Content;
  
  public class Main {
      static int MOD = 1000000007;
  
      // After writing solution, quick scan for:
      //   array out of bounds
      //   special cases e.g. n=1?
      //   npe, particularly in maps
      //
      // Big numbers arithmetic bugs:
      //   int overflow
      //   sorting, or taking max, after MOD
      void solve() throws IOException {
          int T = ri();
          for (int Ti = 0; Ti < T; Ti++) {
              long[] nk = rll(2);
              int n = (int) nk[0];
              long k = nk[1];
  
              int[] a = ril(n);
              sort(a);
  
              long currsum = 0;
              for (int ai : a) currsum += ai;
  
              long need = currsum - k;
              if (need <= 0) {
                  pw.println("0");
                  continue;
              }
              
              long[] suffix = new long[n];
              suffix[n-1] = a[n-1];
              for (int i = n-2; i >= 0; i--) suffix[i] = suffix[i+1] + a[i];
              long ans = need;  // case countop2 = 0
              for (int countop2 = 1; countop2 <= n-1; countop2++) {
                  long sumai = suffix[n-countop2] + a[0];
                  long rhs = need - sumai;
                  long x;
                  if (rhs % (countop2+1) == 0) {
                      x = rhs / (countop2+1);
                      x = -x;
                  } else {
                      if (rhs >= 0) {
                          x = rhs / (countop2+1);
                          x = -x - 1;
                      } else {
                          x = -rhs / (countop2+1);
                      }
                  }
                  ans = Math.min(ans, Math.max(a[0] - x, 0) + countop2);
              }
  
              pw.println(ans);
          }
      }
      // IMPORTANT
      // DID YOU CHECK THE COMMON MISTAKES ABOVE?
  
      // Template code below
  
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter pw = new PrintWriter(System.out);
  
      public static void main(String[] args) throws IOException {
          Main m = new Main();
          m.solve();
          m.close();
      }
  
      void close() throws IOException {
          pw.flush();
          pw.close();
          br.close();
      }
  
      int ri() throws IOException {
          return Integer.parseInt(br.readLine().trim());
      }
  
      long rl() throws IOException {
          return Long.parseLong(br.readLine().trim());
      }
  
      int[] ril(int n) throws IOException {
          int[] nums = new int[n];
          int c = 0;
          for (int i = 0; i < n; i++) {
              int sign = 1;
              c = br.read();
              int x = 0;
              if (c == '-') {
                  sign = -1;
                  c = br.read();
              }
              while (c >= '0' && c <= '9') {
                  x = x * 10 + c - '0';
                  c = br.read();
              }
              nums[i] = x * sign;
          }
          while (c != '\n' && c != -1) c = br.read();
          return nums;
      }
  
      long[] rll(int n) throws IOException {
          long[] nums = new long[n];
          int c = 0;
          for (int i = 0; i < n; i++) {
              int sign = 1;
              c = br.read();
              long x = 0;
              if (c == '-') {
                  sign = -1;
                  c = br.read();
              }
              while (c >= '0' && c <= '9') {
                  x = x * 10 + c - '0';
                  c = br.read();
              }
              nums[i] = x * sign;
          }
          while (c != '\n' && c != -1) c = br.read();
          return nums;
      }
  
      int[] rkil() throws IOException {
          int sign = 1;
          int c = br.read();
          int x = 0;
          if (c == '-') {
              sign = -1;
              c = br.read();
          }
          while (c >= '0' && c <= '9') {
              x = x * 10 + c - '0';
              c = br.read();
          }
          return ril(x);
      }
  
      long[] rkll() throws IOException {
          int sign = 1;
          int c = br.read();
          int x = 0;
          if (c == '-') {
              sign = -1;
              c = br.read();
          }
          while (c >= '0' && c <= '9') {
              x = x * 10 + c - '0';
              c = br.read();
          }
          return rll(x);
      }
  
      char[] rs() throws IOException {
          return br.readLine().toCharArray();
      }
  
      void sort(int[] A) {
          Random r = new Random();
          for (int i = A.length-1; i > 0; i--) {
              int j = r.nextInt(i+1);
              int temp = A[i];
              A[i] = A[j];
              A[j] = temp;
          }
          Arrays.sort(A);
      }
  
      void printDouble(double d) {
          pw.printf("%.16f", d);
      }
  }