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H - Histogram

Score : $600$ points

Problem Statement

Given are integer sequences of length $N$ each: $A = (A_1, \dots, A_N)$ and $C = (C_1, \dots, C_N)$.

You can do the following operation any number of times, possibly zero.

• Choose an integer $i$ such that $1 \leq i \leq N$ and add $1$ to the value of $A_i$, for a cost of $C_i$ yen (Japanese currency).

After you are done with the operation, you have to pay $K \times X$ yen, where $K$ is the number of different values among the elements of $A$.

What is the minimum total amount of money you have to pay?

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq X \leq 10^6$
• $1 \leq A_i, C_i \leq 10^6 \, (1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$

$A_1$ $C_1$

$\vdots$

$A_N$ $C_N$

Output

Print a number representing the answer.

3 5
3 2
2 4
4 3

12

After adding $1$ to $A_1$, there will be two different values among the elements of $A$, for a total cost of $C_1 + 2 \times X = 12$ yen. It is impossible to make the total cost less than this.

1 1
1 1

1

7 7
3 2
1 7
4 1
1 8
5 2
9 8
2 1

29