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Number of Beautiful Partitions

You are given a string s that consists of the digits '1' to '9' and two integers k and minLength.

You are given a string s that consists of the digits '1' to '9' and two integers k and minLength.

A partition of s is called beautiful if:

Return the number of beautiful partitions of s. Since the answer may be very large, return it modulo 10^9 + 7.

A substring is a contiguous sequence of characters within a string.

Number of Beautiful Partitions diagram

Example 1

Input: s = "23542185131", k = 3, minLength = 2

Output: 3

Explanation: There exists three ways to create a beautiful partition: "2354 | 218 | 5131" "2354 | 21851 | 31" "2354218 | 51 | 31"

Example 2

Input: s = "23542185131", k = 3, minLength = 3

Output: 1

Explanation: There exists one way to create a beautiful partition: "2354 | 218 | 5131".

Example 3

Input: s = "3312958", k = 3, minLength = 1

Output: 1

Explanation: There exists one way to create a beautiful partition: "331 | 29 | 58".

Constraints

  • 1 <= k, minLength <= s.length <= 1000
  • s consists of the digits '1' to '9'.

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