2851 - String Transformation.

Hard

You are given two strings s and t of equal length n. You can perform the following operation on the string s:

• Remove a suffix of s of length l where 0 < l < n and append it at the start of s. For example, let s = 'abcd' then in one operation you can remove the suffix 'cd' and append it in front of s making s = 'cdab'.

You are also given an integer k. Return the number of ways in which s can be transformed into t in exactly k operations.

Since the answer can be large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: s = "abcd", t = "cdab", k = 2

Output: 2

Explanation:

First way:

In first operation, choose suffix from index = 3, so resulting s = "dabc".

In second operation, choose suffix from index = 3, so resulting s = "cdab".

Second way:

In first operation, choose suffix from index = 1, so resulting s = "bcda".

In second operation, choose suffix from index = 1, so resulting s = "cdab".

Example 2:

Input: s = "ababab", t = "ababab", k = 1

Output: 2

Explanation:

First way:

Choose suffix from index = 2, so resulting s = "ababab".

Second way:

Choose suffix from index = 4, so resulting s = "ababab".

Constraints:

• <code>2 <= s.length <= 5 * 10⁵</code>

• <code>1 <= k <= 10¹⁵</code>

• s.length == t.length

• s and t consist of only lowercase English alphabets.