CF1622C.Set or Decrease

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).

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 $2 \cdot 10^5$ .

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

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.