Fjölkveradalur

In a remote place in central Iceland there is a forgotten, small, dark
hidden valley called Fjölkveradalur (“the valley with many geysers”). As
the name indicates, the place contains a lot of eruptive hot springs.
But there is something weird about this valley. On the one hand, the
geysers’ regularity cannot be natural: for each geyser, the time between
two of its consecutive eruptions is fixed; moreover, this time, when
expressed in seconds, is always an exact integer number. On the other
hand, some archaic, many-thousand-year-old runes have been found on
strange rocks around the geysers. And according to dating analyses,
these runes were written much before any known human presence in the
island.

These intriguing facts have induced the study and decription of the
runes’ meaning. The astounding conclusion is that, if one day all the
geysers erupt at the same instant, the nearby volcano Hekla
(traditionally known as “the gateway to Hell”) will open its doors and
the world will be anihilated. Since this could be a little bit
disturbing, you are asked to write a program to foresee that moment.

Input

Input consists of several test cases, one per line. Each line has the
description of one or more geysers, each with a pair of natural numbers
p (the length in seconds of the period) and n (the number of seconds
until the next eruption). So, for instance, 3 0 describes a geyser that
erupts every three seconds and that is erupting just now. Assume
0 ≤ n < p ≤ 20.

Output

For every test case, print the number of seconds until the destruction
of the world. If that moment will never arrive or if it is just now,
state so as shown in the examples.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:11:33.223Z

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