Count The Number Of Paths

A program to count the number of distinct trips that can be made from a designated starting station back to itself using a specified number of tickets.  For example given

3 4

0 1

2 1

the out put is 2. displayed in test0.dat

 However given 

100 8

0 1

0 2

0 3

â‹®

0 99

1 2

1 3

â‹®

98 99

The output should be  92274469442793 (test1.dat).

The first line of input fill will contain two integers, N, and k. N is the number of stations in the subway system, 1≤N≤100. k is the number of tickets to be used up, 1≤k≤10.

The question is why the output is not 92274469442793 without using recursion. Only the trip counter function can be altered.