Minimum Same Difference

For an array $A$ of size $N$, we define $f(A)$ as follows: - If $A$ contains $N$ distinct elements, $f(A) = 0$. - Otherwise, $f(A) = \min (j - i)$ among all pairs $(i, j)$ satisfying $1 \le i < j \le N$ and $A_i = A_j$. You are given $2$ integers $N$ and $K$. Your task is to find the sum of $f(A)$ over all arrays $A$ of size $N$ satisfying $1 \le A_i \le K$. Since the answer may be large, prin