World's Worst Bus Schedule

Time Limit: 2 Seconds
Memory Limit: 65536 KB

**Introduction**
You are a very impatient person, and hate to be kept waiting. You are on your
way to visit a relative all the way in New Orleans. The problem is that the bus
station you are at has the world's worst bus schedule! There are no arrival or
departure times listed, only route durations for each bus running. Being the impatient
person you are, you whip out your laptop and attempt to write a program that will
determine how long you will have to wait before the next bus comes. Hey, you have
nothing better to do, right?

**Input**

Input to this problem will consist of a (non-empty) series of up to 100 data
sets. Each data set will be formatted according to the following description,
and there will be no blank lines separating data sets.

A single data set has 3 components:

Start line - A single line, "START N", where N is the number of buses
running and

1 <= N <= 20.

Route Duration line - There will be N of these lines, and each line will consist
of M route durations (where 1 <= M <= 10), which will signify how long
it will take each bus to return to the bus station after completing a particular
route. A route duration will be represented as an integer between 1 and 1000
(inclusive).

Arrival Time - There will only be one of these lines per data set. This line
represents the time that you arrived at the bus station and began waiting. This
is simply the number of time units that you arrived at the bus station after
the buses began running (all buses begin running at time 0). This number is
represented as a positive integer (yes, it can be 0 as well, this would signify
arriving at the bus station as the buses begin running).

End line - A single line, "END".

Following the final data set will be a single line, "ENDOFINPUT".

**Output**

For each data set, there will be exactly one line of output. This line will
simply be the number of time units you will have to wait before the next bus
comes after you arrive. You hate waiting so much that you will just get on the
first bus that returns to the station. Let's hope this is the bus to New Orleans!

Notes

All buses continuously go on their routes, starting back up with their first
route after their last route is done.

If the passenger's arrival time coincides with any of the bus' route departure
times, he/she catches the bus at that time.

** Sample Input**

START 3

100 200 300

400 500 600

700 800 900

1000

END

START 3

100 200 300 4 3 2 4 2 22

800

10 1000

32767

END

ENDOFINPUT

**Sample Output**

200

20

Source:

**South Central USA 2002**
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