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.lang.*;
  import java.io.*;
   
  public class Main
  {
  	PrintWriter out = new PrintWriter(System.out);
  	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
      StringTokenizer tok = new StringTokenizer("");
      String next() throws IOException {
          if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
          return tok.nextToken();
      }
      int ni() throws IOException { return Integer.parseInt(next()); }
      long nl() throws IOException { return Long.parseLong(next()); }
      int[] na(int n) throws IOException { int[]A=new int[n]; for (int i=0;i<n;i++) A[i]=ni(); return A; }
      
      long mod=1000000007;
      
      void solve() throws IOException {
          for (int tc=ni();tc>0;tc--) {
              int n=ni();
              long k=nl();
              Integer[]A=new Integer[n];
              for (int i=0;i<n;i++) A[i]=ni();
              Arrays.sort(A);
              long sum=0;
              for (int v:A) sum+=v;
              
              if (sum<=k) { out.println(0); continue; }
              
              long lt=0;
              long rt=sum-k;
              while (lt+1<rt) {
                  long av=(lt+rt)/2;
                  if (chk(A,av,sum,k,n)) rt=av;
                  else lt=av;
              }
              
              out.println(rt);
          }
          out.flush();
      }
      
      boolean chk(Integer[]A,long z,long sum,long tar,int n) {
          
          long req=0;
          for (int i=n-1;i>0;i--) {
              req++; 
              sum-=(A[i]-A[0]);
              if (req>z) return false;
              if (sum<=tar) return true;
              
              long left=sum-tar;
              long steps=left/(req+1);
              if (left%(req+1)!=0) steps++;
              if (req+steps<=z) return true;
          }
          return false;
      }
      
      int gcd(int a,int b) { return(b==0?a:gcd(b,a%b)); }
      long gcd(long a,long b) { return(b==0?a:gcd(b,a%b)); }
      long mp(long a,long p) { long r=1; while(p>0) { if ((p&1)==1) r=(r*a)%mod; p>>=1; a=(a*a)%mod; } return r; }
      
      public static void main(String[] args) throws IOException {
          new Main().solve();
      }
  }