There are $N$ cities located at nodes $1, 2, \dots, N$. As the city manager, Xiao Ming wants to connect these $N$ cities with the minimum cost. The cost of connecting the cities is divided into the following two types:

Type 1: Constructing a road between city $a$ and city $b$ costs $|a - b|$.

Type 2: Setting up a management city. A city $X$ can be upgraded to a management city at a cost of $C$.

Given the constraints that every road must connect to at least one management city, and each non-management city can be connected to only one edge, Xiao Ming wants to know the minimum cost to connect all cities.

Input

The first line contains a positive integer $N$, representing the number of cities.

The second line contains an integer $C$, representing the cost of setting up a management city.

Output

A single integer representing the minimum cost for Xiao Ming to connect all cities.

Examples

Input 1

6
3

Output 1

12

Input 2

1000
1000

Output 2

32561

Input 3

100000
10000

Output 3

10099799

Note

The minimum cost is achieved by setting cities $2$ and $5$ as management cities and connecting the five edges $(1, 2), (2, 3), (2, 5), (4, 5), (5, 6)$.

Alternatively, setting city $3$ or $4$ as a management city and connecting all other points also achieves the minimum cost.

Constraints

For 20% of the data, $1 \le N \le 20$.

For 40% of the data, $1 \le N \le 10^3$.

For another 20% of the data, $1 \le N \le 10^5, 0 \le C \le 10^4$.

For 100% of the data, $1 \le N \le 10^9, 0 \le C \le 10^9$.