Abacaba#1131
In a lesson at the School of Magic and Wizardry, students learned about the new spell S_{\infty}. This spell is constructed as follows: you start with the empty spell S_0, which contains no letters. Each subsequent spell is formed by first reciting the spell from the previous step, then adding the next letter of the magical alphabet, and finally repeating the previous spell. In other words, S_n = S_{n-1}[n]S_{n-1}, where denotes the -th letter of the magical alphabet. This process theoretically continues indefinitely, but few have managed to recite the entire spell S_{\infty}. Therefore, you are only required to output a certain fragment of the spell S_{\infty}.
The input consists of a single line containing two natural numbers and (1 \leq k \leq 10^{100000}, 1 \leq l \leq 10^6).
Output a fragment of the spell S_{\infty} of length , starting from the -th symbol from the beginning. As there are more letters in the magical alphabet than in any standard encoding, output their ordinal numbers in the magical alphabet instead of letters, separating them by spaces.
Example 1