Codeforces Round #352 (Div. 1) B. Robin Hood （二分）

We all know the impressive story of Robin Hood. Robin Hood uses his archery skills and his wits to steal the money from rich, and return it to the poor.

There are n citizens in Kekoland, each person has c_i coins. Each day, Robin Hood will take exactly 1 coin from the richest person in the city and he will give it to the poorest person (poorest person right after taking richest's 1 coin). In case the choice is not unique, he will select one among them at random. Sadly, Robin Hood is old and want to retire in k days. He decided to spend these last days with helping poor people.

After taking his money are taken by Robin Hood richest person may become poorest person as well, and it might even happen that Robin Hood will give his money back. For example if all people have same number of coins, then next day they will have same number of coins too.

Your task is to find the difference between richest and poorest persons wealth after k days. Note that the choosing at random among richest and poorest doesn't affect the answer.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 500 000, 0 ≤ k ≤ 10⁹) — the number of citizens in Kekoland and the number of days left till Robin Hood's retirement.

The second line contains n integers, the i-th of them is c_i (1 ≤ c_i ≤ 10⁹) — initial wealth of the i-th person.

Output

Print a single line containing the difference between richest and poorest peoples wealth.

Examples

Input

4 1
1 1 4 2

Output

Input

3 1
2 2 2

Output

Note

Lets look at how wealth changes through day in the first sample.

[1, 1, 4, 2]
[2, 1, 3, 2] or [1, 2, 3, 2]

So the answer is 3 - 1 = 2

In second sample wealth will remain the same for each person.

【分析】有n个人，每个人有ai个硬币，有个罗宾汉，每天会从最有钱的人那里偷一个硬币给最穷的人，问你k天后最有钱的人比最穷的人多多少钱。

二分出k次之后的硬币最大值和最小值，然后相减。。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#define inf 0x3f3f3f3f
#define met(a,b) memset(a,b,sizeof a)
#define pb push_back
typedef long long ll;
using namespace std;
const int N = 5e5+10;
const int M = 1e6+10;
ll n,k,tot,MAX,a[N];
int main() {
    scanf("%d %d",&n,&k);
    for(int i = 1; i <= n; i++) scanf("%d",&a[i]),tot += a[i],MAX = max(MAX,a[i]);
    int s = 0,t = tot/n;
    while(s != t) {
        int mid = (s + t)/2 +1;
        long long now = 0;
        for(int i = 1; i <= n; i++)
            if(a[i] < mid) now += mid - a[i];
        if(now > k) t = mid - 1;
        else s = mid;
    }
    int ans1 = s;
    s = (tot + n - 1)/n,t = MAX;
    while(s != t) {
        int mid = (s + t)/2;
        ll now = 0;
        for(int i = 1; i <= n; i++)
            if(a[i] > mid) now += a[i] - mid;
        if(now > k) s = mid + 1;
        else t = mid;
    }
    int ans2 = s;
    cout<<ans2 - ans1<<endl;
}