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: \(f_0 = f_1 = 1\) and \(f_i = f_{i-1}+f_{i-2}\) for all \(i>1\).

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: \(n=f_{i_1}+f_{i_2}+\dots+f_{i_m}\) such that \(i_j>0\) and \(|i_j-i_k|>1\) for all \(1 \le i, j \le m\), \(i \ne j\). For example, let's say \(n=7\), we can represent \(n = 7 = 2 + 5 = f_2 + f_4\), so 7 in Fibonacci number system is 1010, \(n=12\) represented as 10101 and \(n=1\) — 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 \(10^{18}\). You are given L and R, and you want to find a part of the string starting from L up to R.

Input format

Input consists of single line containing two integers L and R (\(1 \le L < R \le 10^{18}\); \(R - L \le 10^5\)).

Output format

Output binary string of length \((R-L)\): \(s_Ls_{L+1}\ldots s_{R-1}\).