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.util.*;
  
  public class Main
  {
  	public static void main(String[] args)throws Exception
  	{
  	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
  	    PrintWriter pw=new PrintWriter(System.out);
  	    int t=Integer.parseInt(br.readLine());
  	    while(t-->0)
  	    {
  	        String s[]=(br.readLine()).split(" ");
  	        int n=Integer.parseInt(s[0]);
  	        long k=Long.parseLong(s[1]);
  	        String s1[]=(br.readLine()).split(" ");
  	        long a[]=new long[n];
  	        long sum=0;
  	        Long A[]=new Long[n];
  	        for(int i=0;i<n;i++)
  	        {
  	            a[i]=Long.parseLong(s1[i]);
  	            A[i]=new Long(a[i]);
  	        }
  	        Arrays.sort(A);
  	        for(int i=0;i<n;i++)
  	        {
  	        	a[i]=(long)A[i];
  	        	sum+=a[i];
  	        }
  	        if(sum<=k)
  	        {
  	            pw.println(0);
  	            continue;
  	        }
  	        long diff=sum-k;
  	        long aSum[]=new long[n];
  	        aSum[n-1]=a[n-1];
  	        for(int i=n-2;i>=0;i--)
  	        {
  	            aSum[i]=aSum[i+1]+a[i];
  	        }
  	        long min=diff;//using only first element 
  	        int num=2;
  	        for(int i=n-1;i>=1;i--)
  	        {
  	            long sum1=aSum[i]+a[0];
  	            long sum2=diff-sum1+a[0]*num;
  	            long x=sum2/num;
  	            if(sum2%num!=0)
  	            {
  	                x++;
  	            }
  	            x=Math.max(x, 0);
  	            if(sum2<0)
  	            {
  	            	x=0;
  	            }
  	            min=Math.min(min,(num-1)+x);
  	            num++;
  	        }
  	        
  	        pw.println(min);
  	        
  	    }
  	    pw.flush();
  	}
  }
  
  
  