Sagheer and Nubian Market

On his trip to Luxor and Aswan, Sagheer went to a Nubian market to buy some souvenirs for his friends and relatives. The market has some strange rules. It containsn different items numbered from 1 to n. The i-th item has base cost a_i Egyptian pounds. If Sagheer buysk items with indices x₁, x₂, ..., x_k, then the cost of itemx_j isa_xj + x_j·k for1 ≤ j ≤ k. In other words, the cost of an item is equal to its base cost in addition to its index multiplied by the factork.

Sagheer wants to buy as many souvenirs as possible without paying more than S Egyptian pounds. Note that he cannot buy a souvenir more than once. If there are many ways to maximize the number of souvenirs, he will choose the way that will minimize the total cost. Can you help him with this task?

Input

The first line contains two integers n andS (1 ≤ n ≤ 10⁵ and1 ≤ S ≤ 10⁹) — the number of souvenirs in the market and Sagheer's budget.

The second line contains n space-separated integersa₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁵) — the base costs of the souvenirs.

Output

On a single line, print two integers k,T — the maximum number of souvenirs Sagheer can buy and the minimum total cost to buy thesek souvenirs.

Example

Input

3 112 3 5

Output

2 11

Input

4 1001 2 5 6

Output

4 54

Input

1 77

Output

0 0

Note

In the first example, he cannot take the three items because they will cost him[5, 9, 14] with total cost 28. If he decides to take only two items, then the costs will be[4, 7, 11]. So he can afford the first and second items.

In the second example, he can buy all items as they will cost him [5, 10, 17, 22].

In the third example, there is only one souvenir in the market which will cost him8 pounds, so he cannot buy it.

题目大意：

在他去卢克索和阿斯旺的旅行中, Sagheer 去了努比亚集市, 为他的亲友们买了一些纪念品。市场有一些奇怪的规则。它包含 n 个从1到 n 的不同项目。该项目有基础成本 ai 埃及镑。如果 Sagheer 购买的 k 项目的指数 x1, x2,..., xk, 那么项目的成本是 axj + xj·k 为1≤ j ≤ k。换言之, 一个项目的成本等于它的基本成本, 除了它的指数乘以 k 的系数。

Sagheer 想买尽可能多的纪念品, 而不用付比埃及镑更多的钱。请注意, 他不能多次购买纪念品。如果有很多方法可以最大限度地增加纪念品的数量, 他会选择将总成本降到最低的方式。你能帮他完成这项任务吗？

#include<stdio.h>#include<string.h>#include<algorithm>#define ll long long intusing namespace std;int main(){    ll n,m;    ll v[100005],dis[100005];    ll l,r,c,mid,sum,sum2;    int i,j;    while(scanf("%lld %lld",&n,&m)!=EOF)    {        sum=0;        memset(dis,0,sizeof(dis));        for(i=1; i<=n; i++)            scanf("%lld",&v[i]);        l=0;        r=n;        while(l<=r)        {            sum=0;            mid=(l+r)/2;            for(i=1; i<=n; i++)            {                dis[i]=v[i]+mid*i;//每次更新单价            }            sort(&dis[1],dis+n+1);//对物品进行价格从低到高排序            for(i=1; i<=mid; i++)                sum+=dis[i];//算出总价            if(sum>m)                r=mid-1;//为了找到一个合适的c不断进行二分            if(sum<=m)            {                sum2=sum;                c=mid;                l=mid+1;            }        }        printf("%lld %lld\n",c,sum2);    }    return 0;}