Problem B
Integer Partition
Input File: pb.in
Time Limit: 5 seconds
A new partition problem is defined as follows. Let the symbol Py,zi be the number of ways to write a positive integer y as a sum of i positive integers having the largest part no larger than z, i.e.,
y = a1+a2+…+ai, and z >= a1 >= a2 … >= ai >= 1
Notice that two sums differing only in the order of their summands are considered to be the same partition. For example, P25,4 = 2 (can be partitioned in two distinct ways: 4+1, 3+2) and P25,3 = 1 (can be partitioned in one single way: 3+2).
Please write a program to compute the number of Piy,z with given integers y, i, and z, which y may be as large as up to 500.
Technical Specification
1. 1 <= y <= 500
2. 1 <= i <= 50
3. 1 <= z <= 100
The first line of the input file contains one integer m(<= 5) indicating the number of test cases to following m lines, there are three integers y, i, and z.
For each test case, output Piy,z.
5 20 4 7 100 50 51 487 18 87 492 19 89 500 19 90
13 204226 7139824136004762 20430740394679891 25985433353057732
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