2156 - Find Substring With Given Hash Value.

Hard

The hash of a 0-indexed string s of length k, given integers p and m, is computed using the following function:

• <code>hash(s, p, m) = (val(s0) * p⁰ + val(s1) * p¹ + ... + val(sk-1) * p^k-1) mod m</code>.

Where val(s[i]) represents the index of s[i] in the alphabet from val('a') = 1 to val('z') = 26.

You are given a string s and the integers power, modulo, k, and hashValue. Return sub, the first substring of s of length k such that hash(sub, power, modulo) == hashValue.

The test cases will be generated such that an answer always exists.

A substring is a contiguous non-empty sequence of characters within a string.

Example 1:

Input: s = "leetcode", power = 7, modulo = 20, k = 2, hashValue = 0

Output: "ee"

Explanation: The hash of "ee" can be computed to be hash("ee", 7, 20) = (5 \* 1 + 5 \* 7) mod 20 = 40 mod 20 = 0. "ee" is the first substring of length 2 with hashValue 0. Hence, we return "ee".

Example 2:

Input: s = "fbxzaad", power = 31, modulo = 100, k = 3, hashValue = 32

Output: "fbx"

Explanation: The hash of "fbx" can be computed to be hash("fbx", 31, 100) = (6 \* 1 + 2 \* 31 + 24 \* 31²) mod 100 = 23132 mod 100 = 32.

The hash of "bxz" can be computed to be hash("bxz", 31, 100) = (2 \* 1 + 24 \* 31 + 26 \* 31²) mod 100 = 25732 mod 100 = 32. "fbx" is the first substring of length 3 with hashValue 32. Hence, we return "fbx".

Note that "bxz" also has a hash of 32 but it appears later than "fbx".

Constraints:

• <code>1 <= k <= s.length <= 2 * 10⁴</code>

• <code>1 <= power, modulo <= 10⁹</code>

• 0 <= hashValue < modulo

• s consists of lowercase English letters only.

• The test cases are generated such that an answer always exists.