115 - Distinct Subsequences.

Hard

Given two strings s and t, return the number of distinct subsequences of s which equals t.

A string's subsequence is a new string formed from the original string by deleting some (can be none) of the characters without disturbing the remaining characters' relative positions. (i.e., "ACE" is a subsequence of "ABCDE" while "AEC" is not).

The test cases are generated so that the answer fits on a 32-bit signed integer.

Example 1:

Input: s = "rabbbit", t = "rabbit"

Output: 3

Explanation: As shown below, there are 3 ways you can generate "rabbit" from s. <code><ins>rabb</ins>b<ins>it</ins></code> <code><ins>ra</ins>b<ins>bbit</ins></code> <code><ins>rab</ins>b<ins>bit</ins></code>

Example 2:

Input: s = "babgbag", t = "bag"

Output: 5

Explanation: As shown below, there are 5 ways you can generate "bag" from s. <code><ins>ba</ins>b<ins> g </ins>bag</code> <code><ins>ba</ins>bgba<ins>g</ins></code> <code><ins> b </ins>abgb**<ins>ag</ins></code> <code>ba<ins> b </ins>gb<ins> ag </ins></code> <code>babg<ins>bag</ins>**</code>

Constraints:

• 1 <= s.length, t.length <= 1000

• s and t consist of English letters.