Number of Ways to Form a Target String Given a Dictionary

You are given a list of strings of the same length words and a string target.

Your task is to form target using the given words under the following rules:

  • target should be formed from left to right.
  • To form the i^th character (0-indexed) of target, you can choose the k^th character of the j^th string in words if target[i] = words[j][k].
  • Once you use the k^th character of the j^th string of words, you can no longer use the x^th character of any string in words where x <= k. In other words, all characters to the left of or at index k become unusable for every string.
  • Repeat the process until you form the string target.

Notice that you can use multiple characters from the same string in words provided the conditions above are met.

Return the number of ways to form target from words. Since the answer may be too large, return it modulo 10^9 + 7.

Example 1
Inputwords = ["acca","bbbb","caca"], target = "aba"
Output6
There are 6 ways to form target using increasing column indices from the given words.
Example 2
Inputwords = ["abba","baab"], target = "bab"
Output4
There are 4 ways to form target using increasing column indices from the given words.

Constraints

  • 1 <= words.length <= 1000
  • 1 <= words[i].length <= 1000
  • All strings in words have the same length.
  • 1 <= target.length <= 1000
  • words[i] and target contain only lowercase English letters.

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