Binary Witch

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Once upon a time in the silent depths of digital forests there lived a Binary
Witch. She was able to forecast weather, telling for any day in the future whether
it will be rainy or sunny.

Her magic was based on the following ancient rule: let a1, a2, ..., aN be the
sequence of binary digits, where ai = 0 indicates that i-th day was rainy, and
ai = 1 - that it was sunny. To predict the weather in day N+1, consider the
t-postfix aN-t+1, aN-t+2, ��, aN consisting of the last t elements. If that postfix
is encountered somewhere before the position N-t+1, i.e. if there is such k
<= N-t, that ak = aN-t+1, ak+1 = aN-t+2, ..., ak+t-1 = aN then the predicted
value will be ak+t.

If there is more than one occurrence of t-postfix, then the rightmost one (with
maximal k) will be taken. So, to make a prediction, she tried t-postfixes, consequently
for t = 13, 12, ..., 1, stopping after the first prediction. If neither postfix
was found, she predicted rain ("0"). If prediction for more than one
day is needed, it is assumed that all previous days are predicted correctly,
so if first predicted value is b, then we make forecast for day N+2 based on
N+1 values, where aN+1 = b.

Because the witch was burned long ago, your task is to write a program to perform
her arcane job.

**Input**

First line of input file contains two integers N (1 <= N <= 1000000)
and L (1 <= L <= 1000), separated by space. Second line contains a string
of N characters "0" and "1".

Process to the end of file.

**Output**

Output file must contain a single string of L characters, which are forecasts
for days N+1, N+2, ..., N+L.

**Sample Input**

10 7

1101110010

**Sample Output**

0100100

Source:

**Northeastern Europe 2000, Far-Eastern Subregion**
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