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.

Contraintes

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.

Exemples

Entrée :
rows = 2
columns = 3

Sortie attendue :
expected = 10

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

Sortie attendue :
long long expected = 10;

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

Sortie attendue :
long expected = 10;

Entrée :
rows = 0
columns = 4

Sortie attendue :
expected = 1

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

Sortie attendue :
long long expected = 1;

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

Sortie attendue :
long expected = 1;

Références

Ce défi a été adapté pour CodeUtility. Suivez l'énoncé et les contraintes ci-dessus.

• #15 Lattice Paths