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 a_{1}, a_{2}, ..., a_{N} be the
sequence of binary digits, where a_{i}=0 indicates that i-th day was rainy, and a_{i}=1 -
that it was sunny. To predict the weather in day N + 1, consider the t-postfix
a_{N-t+1}, a_{N-t+2}, ..., a_{N} consisting of the last t elements. If that postfix is encountered some-
where before the position N - t + 1, i.e. if there is such k ≤ N - t, that
a_{k} = a_{N-t+1}, a_{k+1} = a_{N-t+2}, ..., a_{k+t-1} = a_{N} then the predicted value will be a_{k+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 a_{N+1} = b.

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

Input file format

First line of input file contains two integers N and L, separated by space.
Second line contains a string of N characters "0" and "
1".

Output file format

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