注意数乘可能会引发数据的溢出

下面贴上一个题目，提示自己要注意数据，不要溢出了！

B. Appleman and Card Game

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Appleman has n cards. Each card has an uppercase letter written on it. Toastman must choosek cards from Appleman's cards. Then Appleman should give Toastman some coins depending on the chosen cards. Formally, for each Toastman's cardi you should calculate how much Toastman's cards have the letter equal to letter onith, then sum up all these quantities, such a number of coins Appleman should give to Toastman.

Given the description of Appleman's cards. What is the maximum number of coins Toastman can get?

Input

The first line contains two integers n andk (1 ≤ k ≤ n ≤ 10⁵). The next line containsn uppercase letters without spaces — the i-th letter describes the i-th card of the Appleman.

Output

Print a single integer – the answer to the problem.

Examples

Input

15 10DZFDFZDFDDDDDDF

Output

82

Input

6 4YJSNPI

Output

4

Note

In the first test example Toastman can choose nine cards with letter D and one additional card with any letter. For each card with D he will get 9 coins and for the additional card he will get 1 coin.

paste my code:

#include <bits/stdc++.h>using namespace std;typedef long long LL;const int maxn = 1e5+5;char record[maxn];int main(){    LL cot[28];//改编数据的类型！    for (int i=0; i<26; i++){        cot[i] = 0;    }    LL n, k;//原来是int ,后来改变数据的类型就过了    cin>>n>>k;    for (int i=0; i<n; i++){        cin>>record[i];        cot[record[i]-65]++;    }    sort(cot, cot+26);    int index = 25;    LL sum =0 ;    while (k){        if(k>cot[index]){            k -= cot[index];            sum += cot[index]*cot[index];//虽然不是很理解大数的乘法，但是两个在整数范围内的数相乘，若他们的结果超过了整数的范围，那么就会溢出            index--;        }        else{            sum += k*k;            k = 0;        }    }    cout<<sum<<endl;    return 0;}