MathDB

Square

ABCD

is divided into

n^2

equal small squares by lines parallel to its sides.A spider starts from

A

and moving only rightward or upwards,tries to reach

C

.Every "movement" of the spider consists of

k

steps rightward and

m

steps upwards or

m

steps rightward and

k

steps upwards(it can follow any possible order for the steps of each "movement").The spider completes

l

"movements" and afterwards it moves without limitation (it still moves rightwards and upwards only).If

n=m\cdot l

,find the number of the possible paths the spider can follow to reach

C

.Note that

n,m,k,l\in \mathbb{N^{*}}

with

k<m

4