GAIC Math 2024 Problem 116

Given $M=\{1,2, \ldots, 8\}, A, B$ are two distincet subsets of set $M$, satisfying

(1) The number of elements in set $A$ is fewer than the number of elements in set $B$.

(2) The smallest element in set $A$ is larger than the largest element in set $B$.

Then the total number of ordered pairs $(A, B)$ satisfying these conditions is _____.