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.util.*;
  import java.io.*;
  
  public class Main {
  
      static long startTime = System.currentTimeMillis();
  
      // for global initializations and methods starts here
  
      // global initialisations and methods end here
  
      static void run() {
          boolean tc = true;
          SheetalFastIO r = new SheetalFastIO();
          //FastReader r = new FastReader();
  
          try (OutputStream out = new BufferedOutputStream(System.out)) {
  
              //long startTime = System.currentTimeMillis();
  
              int testcases = tc ? r.ni() : 1;
              int tcCounter = 1;
              // Hold Here Sparky------------------->>>
              // Solution Starts Here
  
              start:
              while (testcases-- > 0) {
  
                  int n = r.ni();
                  long k = r.nl();
                  List<Long> al = new ArrayList<>();
                  for (int i = 0; i < n; i++) al.add(r.nl());
  
                  long sum = 0;
                  for (long ele : al) sum += ele;
  
                  Collections.sort(al);
  
                  Stack<Long> stack = new Stack<>();
                  long first = al.get(0);
                  for (int i = 1; i < n; i++) {
                      long ele = al.get(i);
                      stack.push(ele - first);
                  }
  
                  long count = 0;
                  long ans = Long.MAX_VALUE;
                  while (true) {
                      if (!stack.isEmpty() && sum > k) {
                          long total = (sum - k + count);
                          long ways = count + 1;
                          ans = Math.min(total / ways + count, ans);
                          sum -= stack.pop();
                          count++;
                      } else {
                          break;
                      }
                  }
  
                  if (sum > k) {
                      long total = (sum - k + count);
                      long ways = count + 1;
  
                      count += (total / ways);
                  }
  
                  long res = Math.min(ans, count);
                  out.write((res + " ").getBytes());
                  out.write(("\n").getBytes());
  
  
              }
              // Solution Ends Here
          } catch (IOException e) {
              e.printStackTrace();
          }
      }
  
      static class SheetalFastIO {
          final private int BUFFER_SIZE = 1 << 16;
          private final DataInputStream din;
          private final byte[] buffer;
          private int bufferPointer, bytesRead;
          public BufferedReader br;
          public StringTokenizer st;
  
          public SheetalFastIO() {
              br = new BufferedReader(new InputStreamReader(System.in));
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public SheetalFastIO(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[100000001]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n') break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          public int ni() 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 nl() 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 nd() 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++];
          }
  
          public void close() throws IOException {
              if (din == null) return;
              din.close();
          }
      }
  
      // Here is the main method..
      public static void main(String[] args) throws Exception {
          run();
      }
  
      static int[] readIntArr(int n, SheetalFastIO r) throws IOException {
          int[] arr = new int[n];
          for (int i = 0; i < n; i++) arr[i] = r.ni();
          return arr;
      }
  
      static long[] readLongArr(int n, SheetalFastIO r) throws IOException {
          long[] arr = new long[n];
          for (int i = 0; i < n; i++) arr[i] = r.nl();
          return arr;
      }
  
      static long mod = 998244353;
  
      static long modInv(long base, long e) {
          long result = 1;
          base %= mod;
          while (e > 0) {
              if ((e & 1) > 0) result = result * base % mod;
              base = base * base % mod;
              e >>= 1;
          }
          return result;
      }
  
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          String word() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          String line() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          int ni() {
              return Integer.parseInt(word());
          }
  
          long nl() {
              return Long.parseLong(word());
          }
  
          double nd() {
              return Double.parseDouble(word());
          }
      }
  
      static int MOD = (int) (1e9 + 7);
  
      static long powerLL(long x, long n) {
          long result = 1;
          while (n > 0) {
              if (n % 2 == 1) result = result * x % MOD;
              n = n / 2;
              x = x * x % MOD;
          }
          return result;
      }
  
      static long powerStrings(int i1, int i2) {
          String sa = String.valueOf(i1);
          String sb = String.valueOf(i2);
          long a = 0, b = 0;
          for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
          for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
          return powerLL(a, b);
      }
  
      static long gcd(long a, long b) {
          if (a == 0) return b;
          else return gcd(b % a, a);
      }
  
      static long lcm(long a, long b) {
          return (a * b) / gcd(a, b);
      }
  
      static long lower_bound(int[] arr, int x) {
          int l = -1, r = arr.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (arr[m] >= x) r = m;
              else l = m;
          }
          return r;
      }
  
      static int upper_bound(int[] arr, int x) {
          int l = -1, r = arr.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (arr[m] <= x) l = m;
              else r = m;
          }
          return l + 1;
      }
  
      static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
          graph.get(edge1).add(edge2);
          graph.get(edge2).add(edge1);
      }
  
      public static class Pair implements Comparable<Pair> {
          int first;
          int second;
  
          public Pair(int first, int second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(Pair o) {
              // TODO Auto-generated method stub
              if (this.first != o.first)
                  return (int) (this.first - o.first);
              else return (int) (this.second - o.second);
          }
      }
  
      public static class PairC<X, Y> implements Comparable<PairC> {
          X first;
          Y second;
  
          public PairC(X first, Y second) {
              this.first = first;
              this.second = second;
          }
  
          public String toString() {
              return "(" + first + "," + second + ")";
          }
  
          public int compareTo(PairC o) {
              // TODO Auto-generated method stub
              return o.compareTo((PairC) first);
          }
      }
  
      static boolean isCollectionsSorted(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
          return true;
      }
  
      static boolean isCollectionsSortedReverseOrder(List<Long> list) {
          if (list.size() == 0 || list.size() == 1) return true;
          for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
          return true;
      }
  
  }