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Problems

Fibonacci strings

Fibonacci strings

Time limit 1 second
Memory limit 128 MiB

The Fibonacci string is a string that consists of 0 and 1 and hasn't to ones in a row.

Given the lexicographic number of Fibonacci string, you must build the Fibonacci string itself. The lexicographic number is a number in a lexicographically ordered set (i.e. sorted in a natural way). The numbering starts from one.

Input data

Contains two integers: the length of Fibonacci string n (1n44) and string number k that you must print. It is guaranteed that the string with number k exists.

Output data

Print the k-th Fibonacci string of length n.

Examples

Input example #1
3 3
Output example #1
010
Input example #2
5 5
Output example #2
00101
Source 2010 LKSH. Berendevy Polyany. July. A' Д01