maybe you would have an idea on how to solve the following problem.
John decided to buy his son Johnny some mathematical toys. One of his most favorite toy is blocks of different colors. John has decided to buy blocks of C different colors. For each color he will buy googol (10^100) blocks. All blocks of same color are of same length. But blocks of different color may vary in length.
Jhonny has decided to use these blocks to make a large 1 x n block. He wonders how many ways he can do this. Two ways are considered different if there is a position where the color differs. The example shows a red block of size 5, blue block of size 3 and green block of size 3. It shows there are 12 ways of making a large block of length 11.Each test case starts with an integer 1 ≤ C ≤ 100. Next line consists c integers. ith integer 1 ≤ leni ≤ 750 denotes length of ith color. Next line is positive integer N ≤ 10^15.
This problem should be solved in 20 seconds for T <= 25 test cases. The answer should be calculated MOD 100000007 (prime number).
It can be deduced to matrix exponentiation problem, which can be solved relatively efficiently in O(N^2.376*log(max(leni))) using Coppersmith-Winograd algorithm and fast exponentiation. But it seems that a more efficient algorithm is required, as Coppersmith-Winograd implies a large constant factor. Do you have any other ideas? It can possibly be a Number Theory or Divide and Conquer problem
Please see TopCoder thread for a solution. No one was close enough to find the answer in this thread.