K-Beautiful Subarrays

You are given an array $A$ of size $N$. You may perform at most $M$ operations, where each operation allows you to increase an element of the array by $1$. An array is considered $K$-beautiful if **all** subarrays of size $K$ have **equal** sum of elements. Find the number of ways to make the array $K$-beautiful using no more than $M$ operations. Since the answer can be large, output your answ