Consider all the sequences with length (0 < *N* < 44), containing only the elements 0 and 1, and no two ones are adjacent (110 is not a valid sequence of length 3, 0101 is a valid sequence of length 4). Write a program which finds the sequence, which is on *K*-th place (0 < *K* < 10^{9}) in the lexicographically sorted in ascending order collection of the described sequences.

### Input

The first line of input contains two positive integers *N* and *K*.

### Output

Write the found sequence or −1 if the number *K* is larger then the number of valid sequences.

### Sample

**Problem Author: **Emil Kelevedzhiev

**Problem Source: **Winter Mathematical Festival Varna '2001 Informatics Tournament