Triples

Two positive integers $m$ and $n$ are given, with $5 \le m \le 100$ and $2 \le n \le 100$. For each exponent $j$, define the set of triples

$T_{m,j} = \{(x, y, z) \in \mathbb{N}^3 \mid x \le y \le z \le m,\ x^j + y^j = z^j\}, \quad j = 2, 3, \dots, n$

where $\mathbb{N}$ is the set of nonnegative integers, that is $\mathbb{N} = \{0, 1, 2, \dots\}$.

Compute the sum $S_{m,n}$:

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

Here $\operatorname{card}(T_{m,j})$ is the number of elements of the set $T_{m,j}$.

The first line contains $m$. The second line contains $n$.

Print the value of $S_{m,n}$.