C. Set or Decreasetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer array a_1, a_2, \dots, 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 \sum\limits_{i=1}^{n}{a_i} \le k? (You are allowed to make values of array negative).InputThe first line contains a single integer t (1 \le t \le 10^4) — the number of test cases.The first line of each test case contains two integers n and k (1 \le n \le 2 \cdot 10^5; 1 \le k \le 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, \dots, a_n (1 \le a_i \le 10^9) — the array itself.It's guaranteed that the sum of n over all test cases doesn't exceed 2 \cdot 10^5.OutputFor each test case, print one integer — the minimum number of steps to make \sum\limits_{i=1}^{n}{a_i} \le k.ExampleInput
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
NoteIn 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:   set a_4 = a_3 = 1;  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:   choose a_7 and decrease in by one 3 times; you'll get a_7 = -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.
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

10 0 2 7 
['binary search', 'brute force', 'greedy', 'sortings', '*1600']