Total Characters in String After Transformations I

Given s and t, perform t rounds where each non-'z' character becomes the next letter and each 'z' becomes "ab", and return the final string length modulo 10^9+7. The algorithmic challenge is to avoid explicit expansion (s and t up to 10^5) by modeling per-character growth over time with a DP/recurrence or fast exponentiation to compute the total length efficiently.