Problem Statement

You are given non-negative integers $q,L,R\;(q \in \{ 0,1\}, \; L \leq R)$. Consider a set $S$ that satisfies all of the following conditions.

• $S$ consists of distinct integers between $L$ and $R$, inclusive.
• If $a \in S, \; b \in S, \; a \neq b$, then $a$ and $b$ differ in at least two digits in binary representation. More formally, there exist at least two non-negative integers $i$ such that $\left\lfloor\frac{a}{2^i}\right\rfloor$ and $\left\lfloor\frac{b}{2^i}\right\rfloor$ have different parities.
• Among those satisfying the above two conditions, the number of elements is maximum.

If $q=0$, find the number of elements in such a set $S$. If $q=1$, construct one such set $S$.

For each input file, solve $T$ test cases.

Constraints

• $1 \leq T \leq 2 \times 10^5$
• $0 \leq q \leq 1$
• $0 \leq L \leq R \leq 10^{18}$
• The sum of $q(R-L)$ over all test cases is at most $5\times 10^6$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
case_1
case_2
\vdots
case_T

Each case is given in the following format:

q L R

Output

Output the answers in a total of $T$ lines. The $t$-th line should contain the answer for the $t$-th test case. For each test case, if $q=0$, print the number of elements in a set $S$ that satisfies the conditions. If $q=1$, for a set $S$ that satisfies the conditions, let

$B_i=\begin{cases} 1 \; (S \text{ contains } i) \\ 0 \; (S \text{ does not contain } i) \end{cases}$

and output it in the following format:

B_LB_{L+1}\dotsB_R

If there are multiple sets $S$ that satisfy the conditions, you may print any of them.