Sequence Check

Prereq: Knapsack Intro

Given 2 strings determine how many distinct subsequences of s equal t. A subsequence of s is the original sequence s with some characters deleted. The answer is guaranteed to be less than 2^31-1.

Constraints

1 <= s.length, t.length <= 100001

The strings s and t will only contain lowercase English letters

Examples

Example 1

Input: s = "rabbbit", t = "rabbit"
Output: 3
Explanation:

You can remove any of the 3 middle b values from s to make the t value

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