10357번 - Triples 다국어

Mr. A invites you to solve the following problem:

“Let be \(m\) and \(n\) two positive integers, \(5 \le m \le 100\), \(2 \le n \le 100\). Consider the following sets of triples:

\[T_{m,j} = \left\{ { (x,y,z) \in \mathbb{N}^{3} }|{ x \le y \le z \le m ~ and ~ x^j + y^j = z^j } \right\} ,  j = 2 .. n\]

where \(\mathbb{N}\) is the set of nonnegative integers (\(\mathbb{N}\) = {0, 1, 2, ...}).

The problem asks you to compute the sum \(S_{m,n}\):

\[S_{m,n} = \sum_{j=2}^{n}{card(T_{m,j})}\]

where \(card(T_{m,j})\) is the number of elements of the set \(T_{m,j}\)."

The input file contains a single test. The first line of the input file contains the value of \(m\)and the second line contains the value of \(n\).

The result will be written to standard output.