Data blocks being read by DBMS from the hard drive
are stored in the main memory
in a fixed number of pre-allocated buffers.
Each buffer can hold one data block.
Each buffer can be either free
(does not contain any useful information) or occupied by some data.
When DBMS is going to read data block from the hard drive it has
to decide which buffer to use for data storing.
are any free buffers, then one of them is used for that purpose.
If there are no free buffers, then one of the occupied buffers
has to be flushed to become free, unless it was locked by
some part of DBMS.
The choice of the buffer to flush is critical to DBMS performance.
A lot of different algorithms were developed, LRU (Least Recently
Used) algorithm being the
one used most often. However, your DBMS is
going to implement the Advanced Buffer Management algorithm
which takes advantage
of the fact that maximal
performance is achieved when
a number of consecutive data blocks from the hard drive are read
into consecutive memory buffers.
Buffers are numbered from 1 to N, where N
(1 ≤ N ≤ 100000)
is a total number of buffers.
Each buffer can be in any one of the following states:
free, occupied or locked.
buffer is assigned an integer number from 1 to 9 –
the worthiness of
the currently stored information in that
buffer. The worthiness of
free buffers is considered to be zero. Locked buffers cannot be
neither used nor flushed and their worthiness is undefined.
Having received the request to read K
(1 ≤ K ≤ 10000)
data blocks from the hard drive, Buffer Manager has to choose
K consecutive non-locked
buffers numbered from L to
L+K-1 that have minimal possible sum of their
worthiness, or to report that it is impossible to find K
consecutive non-locked buffers. The latter can also happen
if total number of buffers is less than K.
Your task is to write a program that models the processing
of one request to Buffer Manager using the above algorithm.
The first line of the input contains two integers,
N and K, separated by a space.
Starting from the second line there is a description of a buffers' state.
The state of each buffer is represented by a single character:
- 0 – when the corresponding buffer is free.
- 1 – when the corresponding buffer is occupied
and has worthiness of 1.
- 2 – when the corresponding buffer is occupied
and has worthiness of 2.
- 9 – when the corresponding buffer is occupied
and has worthiness of 9.
- * – when the corresponding buffer is locked.
Those characters are situated on the consecutive lines grouped by 80
characters per line without any spaces. Thus, each line starting
from the second one contains exactly 80 characters with a possible exception
for the last line.
Write to the output the single integer number L.
This number gives the buffer number where first of the
blocks from the hard drive shall be read to ensure the minimal
possible total worthiness of the blocks that
have to be flushed.
If there are more than one such value for L,
then write the smallest one.
Write to the output a single number 0 if it's impossible to find
K consecutive non-locked buffers.
Problem Source: 2000-2001 ACM Northeastern European Regional Programming Contest