Masha likes numbers. She likes Fibonacci numbers even more, so that she represents all natural numbers as sum of Fibonacci numbers. She calls it Fibonacci number system.
Fibonacci numbers is a sequence f, which is defined as follows: and for all .
Numbers in Fibonacci number system are represented as binary strings with no leading zeros and no two ones are consecutive. To represent natural number n in this system, one has to represent n as the sum of non-consecutive Fibonacci numbers: such that and for all , . For example, let's say , we can represent , so 7 in Fibonacci number system is 1010, represented as 10101 and — as 1.
Masha got a piece of paper and started writing a big binary string s. Binary string s is formed as follows: initially she has empty string, then she appends Fibonacci number system representation of every natural number starting with 1 in increasing order. So the beginning of her string looks as follows: 110100101100010011010.... These are numbers from 1 to 7, their Fibonacci number system representations are: 1, 10, 100, 101, 1000, 1001, 1010.
Masha is very patient and hard-working, so she wrote a string s of length . You are given L and R, and you want to find a part of the string starting from L up to R.
Input consists of single line containing two integers L and R (; ).
Output binary string of length : .
These are of Masha's string: 1101001011000100110.