Number Spiral

Source: CSES

Version: Phuoc Hung OJ Extended

Problem Statement

A number spiral is an infinite square grid filled with consecutive positive integers. Row 1, column 1 contains 1. The first five rows and columns are:

 1  2  9 10 25
 4  3  8 11 24
 5  6  7 12 23
16 15 14 13 22
17 18 19 20 21

Given a 1-based row $y$ and column $x$, determine the number in that cell. The spiral continues following the same pattern for all valid coordinates.

Input

One line contains two integers $y$ and $x$, the requested row and column.

Output

Print exactly one integer: the value in row $y$, column $x$.

Subtasks

• Subtask 1 (20%): $1\\le y,x\\le5$.
• Subtask 2 (30%): $1\\le y,x\\le10^4$.
• Subtask 3 (50%): $1\\le y,x\\le10^9$.

Examples

Example 1

Input:

2 3

Output:

8

Explanation: The value in row 2, column 3 of the displayed grid is 8.

Example 2

Input:

1 1

Output:

1

Explanation: The upper-left cell is the start of the spiral and contains 1.

Example 3

Input:

4 2

Output:

15

Explanation: The fourth row begins 16, 15, 14, 13, so column 2 has value 15.