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