Snake

Interview

Time limit1sMemory limit1024 MB

Summary

Given a screen of width N and height M filled by a spiral snake with its head at (0, 0), find the length in cells from the head to body cell (X, Y).

Level: Medium4 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

Mantas likes to play the classic Snake game. The idea is simple: eat apples, grow the snake, and keep its head from hitting its body.

Once, Mantas won the game. The snake lies in a spiral shape, as shown in the picture, and fills every cell of the screen.

Let the head of the snake be at coordinate (0; 0). Given the screen width N and height M, find the length of the snake from the head to the body cell (X; Y).

Figure 1. For N = 6 and M = 6, the length from the head to X = 2, Y = 4 is 28.

Coordinates increase to the right and downward. The length is counted in cells, from the center of the head cell to the center of the given body cell.

Examples2

Example 1
Input
```
6 6 2 4
```
Expected output
```
28
```
Example 2
Input
```
4 3 0 1
```
Expected output
```
9
```