The Toll-Stick of Gorren Bridge

# The Toll-Stick of Gorren Bridge

The keeper of Gorren Bridge records the day on a single stick of yew. For each traveller who crosses, one mark is cut: the number of coins that traveller paid. When a keeper's shift ends, a flat groove is cut instead, the takings are carried off to the strongbox, and the counting begins again from nothing.

The bridge-wardens want to know how far down the stick they must read before a shift's takings first reach the day's quota.

Arguments

• marks — a list of non-negative integers, read left to right. A value of 0 is a groove; any other value is the coins a traveller paid.
• quota — a non-negative integer.

Definitions

The *takings* at a position are the sum of all marks from just after the most recent groove up to and including the mark at that position. A groove's own takings are 0, since nothing has been counted since it.

Return

The 1-based position of the earliest mark whose takings are at least quota. If no position on the stick qualifies, return -1.