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ZOJ Problem Set - 2051
Buffer Manager

Time Limit: 2 Seconds      Memory Limit: 65536 KB

DBMS (Data Base Management System) development team has been successful in designing efficient Lock Manager and is going to proceed further. As a part of the team you will be responsible for the Buffer Manager.

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. If there 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. Each occupied buffer is assigned an integer number from 1 to 9 �C 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.


Input

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 �C when the corresponding buffer is free.
1 �C when the corresponding buffer is occupied and has worthiness of 1.
2 �C when the corresponding buffer is occupied and has worthiness of 2.
...
9 �C when the corresponding buffer is occupied and has worthiness of 9.
* �C 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.


Output

Write to the output the single integer number L. This number gives the buffer number where first of the K 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.


This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.


Sample Input

2

100 53
2165745216091853477755800393859785807207523169954341**7363*9*94664808*4777717089
09825185827659480548

100 10
2165745216091853477755800393859785807207523169954341**7363*9*94664808*4777717089
09825185827659480548


Sample Output

0

36


Source: Northeastern Europe 2000
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