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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.PrintWriter;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.Random;
  import java.util.StringTokenizer;
  
  public class c {
  	public static void main(String[] args) {
  		FastScanner scan=new FastScanner();
  		PrintWriter out=new PrintWriter(System.out);
  
  		int t=scan.nextInt();
  		for(int tt=0;tt<t;tt++) {
  			int n=scan.nextInt();
  			long k=scan.nextLong();
  			long sum=0;
  			long[] a=new long[n];
  			for(int i=0;i<n;i++) {
  				a[i]=scan.nextLong();
  				sum+=a[i];
  			}
  			ruffleSort(a);
  			long res=Long.MAX_VALUE;
  			long suffix=0, leave=0;
  			for(long take=0;take<n;take++) {
  				long lo=(long)(-1*1e15), hi=a[0];
  				long best=Long.MIN_VALUE;
  				while(hi>=lo) {
  					long mid=(hi+lo)>>1;
  					long cur=sum-(a[0]-mid);
  					if(mid<0&&Math.abs(Long.MAX_VALUE/mid)<take)  {
  						best=Math.max(best,mid);
  						lo=mid+1;
  					}
  					else {
  						leave=mid*take;
  						cur-=suffix-leave;
  						if(cur<=k) {
  							best=Math.max(best,mid);
  							lo=mid+1;
  						}
  						else hi=mid-1;
  					}
  				}
  				if(best==Long.MIN_VALUE) continue;
  				res=Math.min(res,a[0]-best+take);
  				suffix+=a[n-(int)take-1];
  			}
  			out.println(res);
  		}
  		out.close();
  	}
      static void ruffleSort(long[] a) {
          Random get = new Random();
          for (int i = 0; i < a.length; i++) {
              int r = get.nextInt(a.length);
              long temp = a[i];
              a[i] = a[r];
              a[r] = temp;
          }
          Arrays.sort(a);
      }
  	static class FastScanner {
  		BufferedReader br;
  		StringTokenizer st;
  
  		public FastScanner() {
  			try	{
  				br = new BufferedReader(new InputStreamReader(System.in));
  				st = new StringTokenizer(br.readLine());
  			} catch (Exception e){e.printStackTrace();}
  		}
  
  		public String next() {
  			if (st.hasMoreTokens())	return st.nextToken();
  			try {st = new StringTokenizer(br.readLine());}
  			catch (Exception e) {e.printStackTrace();}
  			return st.nextToken();
  		}
  
  		public int nextInt() {return Integer.parseInt(next());}
  
  		public long nextLong() {return Long.parseLong(next());}
  
  		public double nextDouble() {return Double.parseDouble(next());}
  
  		public String nextLine() {
  			String line = "";
  			if(st.hasMoreTokens()) line = st.nextToken();
  			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
  			while(st.hasMoreTokens()) line += " "+st.nextToken();
  			return line;
  		}
  	}
  }
  