CF1244E.Minimizing Difference

You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ integers.

You may perform the following operation on this sequence: choose any element and either increase or decrease it by one.

Calculate the minimum possible difference between the maximum element and the minimum element in the sequence, if you can perform the aforementioned operation no more than $k$ times.

给你一个由 $n$ 个整数组成的序列 $a_1, a_2, \dots, a_n$。

你可以对这个序列执行以下操作：任选一个元素，并将其加一或减一。

如果你最多可以执行上述操作 $k$ 次，求序列中最大值与最小值之间可能的最小差值。

The first line contains two integers $n$ and $k$ $(2 \le n \le 10^{5}, 1 \le k \le 10^{14})$ — the number of elements in the sequence and the maximum number of times you can perform the operation, respectively.

The second line contains a sequence of integers $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 10^{9})$.

第一行包含两个整数 $n$ 和 $k$ $(2 \le n \le 10^{5}, 1 \le k \le 10^{14})$ —— 分别表示序列中元素的个数以及你最多可以执行该操作的次数。

第二行包含一个整数序列 $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 10^{9})$。

Print the minimum possible difference between the maximum element and the minimum element in the sequence, if you can perform the aforementioned operation no more than $k$ times.

输出在最多执行 $k$ 次上述操作的前提下，序列中最大元素与最小元素之间的最小可能差值。

In the first example you can increase the first element twice and decrease the third element twice, so the sequence becomes $[3, 3, 5, 5]$, and the difference between maximum and minimum is $2$. You still can perform one operation after that, but it's useless since you can't make the answer less than $2$.

In the second example all elements are already equal, so you may get $0$ as the answer even without applying any operations.

在第一个例子中，你可以将第一个元素增加两次，并将第三个元素减少两次，从而使序列变为 $[3, 3, 5, 5]$，此时最大值与最小值之差为 $2$。此后你仍可执行一次操作，但这已无意义，因为你无法使答案小于 $2$。

在第二个例子中，所有元素已经相等，因此即使不执行任何操作，答案也可为 $0$。