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

 

lucas