Solution: Distinct Subsequences

Statement

Given two strings, s and t, determine how many distinct subsequences of s match t exactly.

Note: A subsequence is formed by deleting zero or more characters from s without changing the relative order of the remaining characters.

You may assume the result will always fit within a $32$-bit signed integer.

Constraints:

• $1 \leq$ s.length, t.length $\leq 1000$ ...