I was solving a problem in which i need to figure out the prime factorization of $\frac{a!}{b!}$ and i did that by computing (a!) and then (b!) by looping ((1 to a) & (1 to b)) and then derived **n** by dividing them ($n = \frac{a!}{b!}$) and then prime factors of n, but it gives me to TLE(Time limit exceeded) so i refered editorial and in editorial they describe an alternate method , they says
**factorization of number $\frac{a!}{b!}$ is this same as factorization of numbers $(b + 1)\times(b + 2)\times \cdots\times (a - 1)\times a$.**

I am unable to figure out how

$\frac{a!}{b!}$ == $(b + 1)\times(b + 2)\times \cdots\times (a - 1)\times a$ ?