There is a queue with N
people. Every person has a different heigth. We can see P people, when we are
looking from the beginning, and R people, when we are looking from the end.It’s
because they are having different height and they are covering each other. How
many different permutations of our queue has such a interesting feature?
The input
consists of T test cases. The number of them (1<=T<=10000)
is given on the first line of the input file.
Each test
case consists of a line containing three integer numbers: N that
indicates the number of people in a queue (1 <= N <= 13), and
then two more integers. The first corresponds to the
number of people, that we can see looking from the beginning, and the second corresponding to the number of people,
that we can see looking from the end.
For every
test case your program has to determine one integer. Print how many
permutations of N people we can see exactly P people from the beginning, and R
people, when we are looking from the end.
3
10 4 4
11 3 1
3 1 2
90720
1026576
1