# Largest Deep Sum

### Wolfram Language (Mathematica), 36 bytes

```
#[email protected]#&@Total[#,{-#2,-1}]&
```

Try it online!

Returns an array containing all the indices where the maximum value can be found. So for normal inputs that's a singleton array, containing the list of indices to it. If there's a tie, you'll get all the lists of indices for where that value shows up.

The function doesn't actually read the `n`

parameter, because it isn't needed, but you could pass it in as a third argument if you like (it would just be ignored anyway).

One catch here is that for some reason the dimension specification `{0,-1}`

for `Total`

never sums anything. I don't really understand why, but luckily that's just what we need for this challenge.

## APL (Dyalog), 21 bytes

```
(⍴⊤⊃∘⍒∘,)+/,⍤⎕⊢⎕
```

First input is the array, second is `p`

.

Try it online!

**How?**

`+/,⍤⎕`

- apply sum over sub arrays of rank `p`

`⊃∘⍒∘,`

- flatten, grade down and take first

`⍴⊤`

- encode in the mixed base derived by the shape of the previous result