Sum Every Element of an N-Dimensional Array Readable Only by Index Lists

You are given an object `m` of type `MultiDimArray` that represents an array with an arbitrary number of dimensions. How the elements are stored is hidden; the object exposes only two methods: - `m.getDims()` returns a list with the size of each dimension. For a 2 × 2 × 3 array it returns `[2, 2, 3]`. - `m.get(indices)` takes a list with one index per dimension and returns the integer stored at that position. For the same array, `m.get([0, 1, 2])` returns the element at index 0 of the first dimension, index 1 of the second and index 2 of the third. Implement `arraySum`, which returns the sum of all elements of the array. ### Function Signature ```python def arraySum(m: MultiDimArray) -> int: ``` ### Rules - Read the array only through `m.getDims()` and `m.get(indices)`; the object offers no other access to its elements. - `m.get(indices)` accepts a list of exactly `len(dims)` integers with `0 <= indices[i] < dims[i]` for every `i`, and raises an error for any other list. - Return the exact integer sum of all elements, counting every position once. - In the examples, an array is written as its dimension sizes plus its elements in row-major order, meaning the last index changes fastest: for `dims = [2, 2, 3]` the elements are listed for positions `[0, 0, 0]`, `[0, 0, 1]`, `[0, 0, 2]`, `[0, 1, 0]`, and so on up to `[1, 1, 2]`. This listing only describes the test input; `m` does not expose it. ### Constraints - `1 <= len(dims) <= 20` - `dims[i] >= 1` for every dimension - The total number of elements, the product of all `dims[i]`, is at most `2 * 10^5`. - Every element is an integer with `-10^9 <= element <= 10^9`. - The sum can reach `2 * 10^14` in absolute value, which is beyond `2^31 - 1` but within `±2^53`. ### Examples **Example 1** ```text Input: m with dims = [2, 2, 3] and elements in row-major order [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] Output: 78 ``` Here `m.getDims()` returns `[2, 2, 3]`, `m.get([0, 1, 2])` returns `6`, and `m.get([1, 0, 0])` returns `7`. The twelve elements add up to 78. **Example 2** ```text Input: m with dims = [4] and elements [3, -1, 4, -1] Output: 5 ``` A one-dimensional array: `3 - 1 + 4 - 1 = 5`. **Example 3** ```text Input: m with dims = [1, 2, 1, 2] and elements in row-major order [1000000000, -5, 1000000000, 1000000000] Output: 2999999995 ``` The four positions are `[0, 0, 0, 0]`, `[0, 0, 0, 1]`, `[0, 1, 0, 0]` and `[0, 1, 0, 1]`. The sum exceeds `2^31 - 1`.