Problem Statement

There are $N$ pieces of sushi. Each piece has two parameters: "kind of topping" $t_i$ and "deliciousness" $d_i$. You are choosing $K$ among these $N$ pieces to eat. Your "satisfaction" here will be calculated as follows:

• The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".
• The base total deliciousness is the sum of the deliciousness of the pieces you eat.
• The variety bonus is $x*x$, where $x$ is the number of different kinds of toppings of the pieces you eat.

You want to have as much satisfaction as possible. Find this maximum satisfaction.

Constraints

• $1 \leq K \leq N \leq 10^5$
• $1 \leq t_i \leq N$
• $1 \leq d_i \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
t_1 d_1
t_2 d_2
.
.
.
t_N d_N

Output

Print the maximum satisfaction that you can obtain.