The strings X[1 ... n) and Y [1 ... m) are given. Our goal is to convert the string X[1 ... n) to the string Y [1 ... m] with the least cost. The cost of adding a new character is TL, the cost of deleting an existing character is TL, and the cost of converting an x character to a y character is f(x, y) dollars. Where k and t are given positive integers, f(x, y) is a positive integer value function. Write down the recurrence required to solve the problem using dynamic programming