1622C · Set or Decrease

Problem: You 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).

Input Format: The 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 $2 \cdot 10^5$.

Output Format: For each test case, print one integer — the minimum number of steps to make $\sum\limits_{i=1}^{n}{a_i} \le k$.

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 $a_4 = 0$.

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 $a_7 = -2$.