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 Solution {
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
          int nextInt() {
              return Integer.parseInt(next());
          }
          long nextLong() {
              return Long.parseLong(next());
          }
          double nextDouble() {
              return Double.parseDouble(next());
          }
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
      static void sort(long a[]){ // int -> long
          ArrayList<Long> arr=new ArrayList<>(); // Integer -> Long
          for(int i=0;i<a.length;i++)
          arr.add(a[i]);
          Collections.sort(arr);
          for(int i=0;i<a.length;i++)
          a[i]=arr.get(i);
          
      }
      private static long gcd(long a, long b){
          if(b==0)return a;
          return gcd(b,a%b);
      }
      private static long pow(long x,long y){
          if(y==0)return 1;
          long temp = pow(x, y/2);
          if(y%2==1){
              return x*temp*temp;
          }
          else{
              return temp*temp;
          }
      }
      static int log(long n){
          int res = 0;
          while(n>0){
              res++;
              n/=2;
          }
          return res;
      }
  
      static int mod = (int)1e9+7;
      static long INF = (long)1e15;
      static PrintWriter out;
      static FastReader sc ;
      public static void main(String[] args) throws IOException {
          sc = new FastReader();
          out = new PrintWriter(System.out);
          // primes();
          // ================================ //
          int test = sc.nextInt();
          while (test-- > 0) {
              int n = sc.nextInt();
              long k = sc.nextLong();
              long[]arr = new long[n];
              for(int i=0;i<n;i++){
                  arr[i] = sc.nextInt();
              }
              solver(arr, n, k);
          }
          // ================================ //
          // int n = sc.nextInt();
          // solver();
          // ================================ //
          out.flush();
      }
  
      public static void solver(long[]arr, int n, long k) {
          long sum = 0;
          long min = INF;
          for(int i=0;i<n;i++){
              min = Math.min(min, arr[i]);
              sum+=(long)arr[i];
          }
          if(sum<=k){
              out.println(0);
              return;
          }
          sort(arr);
          long[]pre = new long[n+1];
          for(int i=1;i<=n;i++){
              pre[i] = pre[i-1]+arr[i-1];
          }
          long res = INF;
          for(int i=1;i<=n;i++){
              long temp = (k-pre[i]+pre[1])/(n-i+1);
              if(temp*(n-i+1)+pre[i]-pre[1]>k)temp--;
              temp = Math.min(temp, arr[0]);
              // System.out.println(i+"__"+ temp);
              res = Math.min(res, (n-i)+(arr[0]-temp));
          }
          out.println(res);
      }
  
      static long check(long[]arr, long sum, long min, long k){
          int n = arr.length;
          if(min*n>k)return INF;
          long res = 0;
          sum-=(arr[0]-min);
          for(int i=n-1;i>=1;i--){
              if(sum<=k)break;
              sum-=(arr[i]-min);
              res++;
              if(sum<=k)break;
          }
          // System.out.println(arr[0]+"__"+    min);
          // System.out.println((arr[0]-min)+"__"+    res);
          return res+(arr[0]-min);
      }
  }
  