Number of Ways to Form a Target String Given a Dictionary

Count the number of ways to form target left-to-right by picking each target character from some word’s character at column k, with the constraint that once you use column k you cannot use any column ≤ k thereafter (columns must be strictly increasing). This is a combinatorics/DP problem that uses per-column letter frequencies to count valid sequences of column-and-word choices, returning the result modulo 10^9+7.