Cow Food    cowfood.X

The nutrition scientists are running experiments on the optimal
herb mixture for feeding cows. They gathered K (2 <= K <= 30) sorts
of different plants and mixed them in formulas represented as a
vector (a_1, a_2, ..., a_K), where a_i is the quantity of plants
of type i used in the mixture. It is known that a_1 + a_2 + ... +
a_K is less than or equal to a given value S (2 <= S <= 10,000).

Each of N (0 <= N <= 20) experiments that the scientists ran proved
to be unsuccesful, as the cows didn't agree with the herb quantities.
Furthermore, they said that for any unsuccesful experiment (a_1,
a_2, ..., a_K) , an experiment (b_1, b_2, ..., b_K) with a_1 <=
b_1, a_2 <= b_2, ..., a_K <= b_K would still fail.

As the scientists want to finish their work as soon as possible,
it is your job to find out how many experiments that might still
have a chance to succeed are left.

You should note that any valid mixture contains at least two nonzero
quantities of different herbs.

PROBLEM NAME: cowfood

INPUT FORMAT:

* Line 1: Three space separated integers: K, S and N

* Lines 2..N + 1: Line i+1 contains K numbers each (a_1, a_2, ...,
        a_K) representing unsuccessful experiment #i.

SAMPLE INPUT:

2 5 2
1 3
3 1

OUTPUT FORMAT:

* Line 1: A single integer that is the number of remaining mixtures
        that cows might still agree with, modulo 3210121.

SAMPLE OUTPUT:

4

OUTPUT DETAILS:

The four remaining mixtures are (1, 1), (1, 2), (2, 1), (2, 2).