The ancient and bustling city of Cnossos was renowned for its mysterious labyrinth, composed of a set of $$$N \times M$$$ square rooms arranged in an $$$N$$$ by $$$M$$$ grid. The rooms were named by an ordered pair $$$(A,B)$$$, where $$$A$$$ represented the row and $$$B$$$ represented the column in which the room was located. The entrance to the labyrinth was at position $$$(1,1)$$$.

In this city, there was a fearless adventurer named Gusteseu. He was known for his courage and skill in unraveling the most complex riddles.

One day, Gusteseu received an extraordinary mission: to explore the labyrinth and find a legendary treasure rumored to be hidden in its depths. However, there was a daunting challenge in Gusteseu's path. The labyrinth was inhabited by a creature feared by all: the mighty Maynotauro.

The Maynotauro, a creature with the body of a woman and the head of a bull, guarded the labyrinth's entrance and protected the path to the treasure. Its dwelling was known as the Maynotauro's room, located at position $$$(X,Y)$$$ in the labyrinth.

Determined to complete his mission, Gusteseu knew he had to avoid the Maynotauro's room. He understood that passing through that room would result in his capture and failure in the quest for the treasure.

Due to the unpleasant conditions within the labyrinth, Gusteseu aimed to reach the treasure room as efficiently as possible, passing through the fewest number of rooms. He disregarded any other ways of achieving this path.

With his sharp mind and expertise in competitive programming, Gusteseu decided to employ his skills to calculate the number of efficient ways to reach the treasure room, located at position $$$(N,M)$$$, without passing through the Maynotauro's room.