链接：https://codeforces.com/contest/1244/problem/E

You are given a sequence a1,a2,…,ana1,a2,…,an consisting of nn 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 kk times.

Input

The first line contains two integers nn and kk (2≤n≤105,1≤k≤1014)(2≤n≤105,1≤k≤1014) — 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 a1,a2,…,ana1,a2,…,an (1≤ai≤109)(1≤ai≤109).

Output

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 kk times.

Examples

input

Copy

4 5
3 1 7 5

output

Copy

2

input

Copy

3 10
100 100 100

output

Copy

0

input

Copy

10 9
4 5 5 7 5 4 5 2 4 3

output

Copy

1

Note

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][3,3,5,5], and the difference between maximum and minimum is 22. You still can perform one operation after that, but it's useless since you can't make the answer less than 22.

In the second example all elements are already equal, so you may get 00 as the answer even without applying any operations.

题解：

#include<bits/stdc++.h>
using namespace std;
long long n,m,ans,l,r;
long long a[100001];
int main()
{
	cin>>n>>m;
	for(int i=1;i<=n;i++)
	cin>>a[i];
	sort(a+1,a+1+n);
	for(int i=1;i<=n/2;i++)
	{
        int j=n-i+1;
        r=(a[i+1]-a[i]+a[j]-a[j-1])*i;
        if(r<=m) 
		m-=r;
        else
		{
            ans=a[j]-a[i]-m/i;
            break;
        }
    }
    cout<<ans;
}