Take any random bitstring containing a sequence of $$m \in \mathbb{N}_0$$ zeros and ones. Place the zeros and ones of the bitstring clockwise around a circle. Reproduce the circle a second time, concentrically with the first circle. Rotate the inner circle over $$n \in \mathbb{Z}$$ places. If $$n > 0$$ the inner circle is rotated clockwise over $$n$$ places. If $$n < 0$$ the inner circle is rotated counterclockwise over $$|n|$$ places.

rotations
Two concentric circles with bits of the bitstring 001011101010011110011010010, where the bits of the inner circle have been rotated clockwise over 14 places.

Now count the number of places where both circles have a zero opposite a one.

pairs
The number of zeros opposite ones will always be even.

This will always yield an even number.

Input

A line containing a bitstring that exists of $$m \in \mathbb{N}_0$$ successive zeros and ones, followed by another line containing a number $$n \in \mathbb{Z}$$.

Output

A line containing the given bitstring, followed by a line containing the given bitstring that is rotated over $$n$$ places. In between these two lines is another line that marks each of the $$m$$ corresponding places with vertical bars (|) where zeros are opposite ones or with spaces where this is not the case. Following these $$m$$ vertical bars and spaces is another space and between round brackets the number of places where zeros are opposite ones.

Example

Input:

001011101010011110011010010
14

Output:

001011101010011110011010010
|| ||| |||| ||||  |     ||  (16)
111100110100100010111010100

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