Binary String Transformation

Given a binary string \( s = s_{1}s_{2}\cdots s_{n} \) consisting of characters '0' and '1', you are to perform a transformation on the string repeatedly.

The transformation is defined as follows:

$$ \begin{aligned} &s'_{1} = s_{1},\\ &s'_{i} = s_{i-1} \oplus s_{i} \quad \text{for } 2 \le i \le n, \end{aligned} $$

where \( a \oplus b \) denotes the bitwise XOR operation (i.e. the result is 0 if \( a = b \) and 1 if \( a \neq b \)).

You will be given an integer \( t \), and you must determine the state of the string after applying the transformation exactly \( t \) times.

inputFormat

The first line contains two integers \( n \) and \( t \) where \( n \) is the length of the binary string and \( t \) is the number of transformations to apply.

The second line contains a binary string of length \( n \) composed only of the characters '0' and '1'.

outputFormat

Output the binary string after applying the transformation \( t \) times.

sample

3 1
011

010

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