The Hedge-Witches of the Thornwall

Commission of the Coven of Brackenmoor.

The Thornwall is a living hedge that rings the borderland against whatever walks out of the Gloamwood. Each dusk every segment of it must be sung shut, and each segment demands a known number of verses.

The Coven sends out a number of hedge-witches together. Each witch is given one unbroken stretch of consecutive segments and sings all of them. Every segment must be sung by exactly one witch. A witch may be given no segments at all. The Coven wants the division that makes the heaviest stretch (the one with the most verses in total) as light as possible.

The contract. Write heaviestStretch(wards, witches).

• wards is a list of non-negative integers: the verses each segment needs, in order along the wall. It may be empty.
• witches is a positive integer.

Split wards into at most witches contiguous groups. Keep the original order, and put every element in exactly one group. Among all such splits, find the one whose largest group sum is smallest, and return that largest group sum as an integer. If wards is empty, return 0.