Number Spiral Lookup

The infinite spiral starts at the top-left cell. The first four rows and columns are shown below. Continue the same pattern in expanding square layers. Coordinates start at 1.

 1   2   9  10
 4   3   8  11
 5   6   7  12
16  15  14  13

Return one cell value without constructing the entire grid.

Implement number_spiral(row, column).

Input

row: The row counted from the top, starting at 1.

column: The column counted from the left, starting at 1.

Output

Return the number at that position.

Restrições

1 ≤ row, column ≤ 1,000,000,000. The value fits a signed 64-bit integer.

Exemplos

Entrada:
row = 3
column = 2

Saída esperada:
expected = 6

Entrada:
long long row = 3;
long long column = 2;

Saída esperada:
long long expected = 6;

Entrada:
long row = 3;
long column = 2;

Saída esperada:
long expected = 6;

Entrada:
row = 1
column = 4

Saída esperada:
expected = 10

Entrada:
long long row = 1;
long long column = 4;

Saída esperada:
long long expected = 10;

Entrada:
long row = 1;
long column = 4;

Saída esperada:
long expected = 10;

Referências

Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.

• Number Spiral — 1071