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# Cipher challenge

Problem statement
Jack and Daniel are friends. They want to encrypt their conversation so that they can save themselves from interception by a detective agency. So they invent a new cipher. Every message is encoded to its binary representation $B$ of length $N$. Then it is written down $K$ times, shifted by $0,1,\dots, K-1$ bits.
If $B=1001010$ and $K=4$ it looks so:

Then calculate XOR in every column and write it down. This number is called $S$. For example, XOR-ing the numbers in the above example results in

Then the encoded message $S$ and $K$ are sent to Daniel.

Jack is using this encoding algorithm and asks Daniel to implement a decoding algorithm.
Can you help Daniel implement this?

Input Format
The first line contains two integers $N$ and $K$.
The second line contains string $S$ of length $N+K+1$ consisting of ones and zeros.

Output Format
Decoded message of length $N$, consisting of ones and zeros.

Constraints
$1 \le N \le N^{6}$
$1 \le K \le N^{6}$
$|S| = N + K - 1$
It is guaranteed that $S$ is correct.

Sample Input#00

Sample Output#00

Sample Input#01

Sample Output#01

Explanation
Input#00

Input#01

Solution