Count Grid Paths

Start at the top-left corner of a grid with rows by columns cells. Move along cell edges only, one edge right or one edge down at a time, until reaching the bottom-right corner. Count distinct move sequences. The grid has no obstacles.

A grid with 2 rows and 3 columns of cells needs exactly 2 down moves and 3 right moves.

Implement lattice_paths(rows, columns).

Input

rows: The number of rows of cells, not vertices.

columns: The number of columns of cells, not vertices.

Output

Return the number of corner-to-corner routes.

制約

0 ≤ rows, columns ≤ 30 and rows + columns ≤ 60. Zero in one dimension gives a straight route. A 0 × 0 grid has one empty route. Counts fit signed 64-bit.

例

入力：
rows = 2
columns = 3

期待される出力：
expected = 10

入力：
long long rows = 2;
long long columns = 3;

期待される出力：
long long expected = 10;

入力：
long rows = 2;
long columns = 3;

期待される出力：
long expected = 10;

入力：
rows = 0
columns = 4

期待される出力：
expected = 1

入力：
long long rows = 0;
long long columns = 4;

期待される出力：
long long expected = 1;

入力：
long rows = 0;
long columns = 4;

期待される出力：
long expected = 1;

参考資料

この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。

• #15 Lattice Paths