Write a Java program that uses a modified version of Algorithm 2.9 (Large Integer Multiplication) so that it divides each n-digit integer into three smaller integers of n/3 digits (you may assume that n = 3k). The Java program and the corresponding function(s) should be flexible enough to deal with different cases and example data should be provided in the main function of this Java program to check its correctness. You must use the divide and conquer strategy to solve this problem, other strategies will not be graded.

Large Integer Multiplication Problem: Multiply two large integers, u and v. Inputs: large integers u and v. Outputs: prod, the product of u and v