The one of the binary search

You are on holidays in the United States, in a highway in the middle of
nothing (for instance, Ohio), driving one of those big cars where a
whole football team would fit. Bored, you decide to discover what
contanst speed you must mantain to reach the next petrol station as soon
as possible. Remember: the greater the speed is, the greater the
consumption is, so if when you arrive to the petrol station the car has
still fuel, it means that you did not go fast enough (OIE recommends a
responsible driving in the real life.).

In particular, you know that your vehicle consumes

$$500 + \lfloor \frac{v+w}{10}\rfloor + \lfloor\frac{(v+w)^2}{100000}\rfloor$$

millilitres of fuel to go around a kilometre, where 0 < v < 30000 and
−3000 < w < 3000 is the speed of the vehicle and the power of the wind
in centimetres per second, and the symbols ⌊⋅⌋ mean round towards zero.
(Certainly, these american cars consume a lot).

You are asked to, given the quantity of fuel that you have, the number
of kilometres of distance to the petrol station, and the intensity of
the wind in each one of the kilometres, say what speed in centimetres
per second you should go all the travel to reach as soon as possible the
petrol station, without being with no fuel during the travel.

Input

A test data contains various cases, separated by a line in white. A case
is described by various lines. The first one contains two numbers
C < 10⁹ and n < 10³, separated by spaces, that describe the quantity of
fuel tha you have and the number of stretches that separe you from the
petrol station. The following n lines describe a road stretch, formed by
a pair of numbers d_(i) and w_(i), with the length in kilometres and the
power of the wind in the i-th strecth. It is fulfilled that
$\sum_{i=1}^n d_i < 10^5$. The consumption of fuel in each kilometre of
a stretch must be computed individually, to avoid rounding problems.

Output

For each case, your program must print in a line the speed in centimetre
per second that would allow you to reach before to the petrol station
without being with no fuel during the travel. We assure you that this
number is greater than 0 and less tan 30000.

Hint: Binary search is that invent that allow us to find a word in the
dictionary without reading all the words.

Author: Ricardo Martín, Omer Giménez.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T12:18:24.575Z

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