AMO · 2027 · Grades 8-9 · Self-study SET 21 Question 2

Suppose the product $\frac{98}{100}\times\frac{97}{99}\times\frac{96}{98}\times\cdots\times\frac35\times\frac24\times\frac13$ is $\frac ab$ in simplest form, with positive integers $a,b$. Find $a+b-4000$.