MEX vs OR

A sequence $a$ of non-negative integers is given. The function $\text{mex}(a)$ is the smallest non-negative integer that is not contained in $a$.

Examples of applying mex to a sequence:

• $\text{mex}([1,2,3,4,5])=0$
• $\text{mex}([0,1,2,3,4])=5$
• $\text{mex}([0,1,2,4,5])=3$

For non-negative integers $x$ and $y$, the bitwise OR $x\,|\,y$ is defined by these rules:

• If at least one of $x$ and $y$ has a 1 in the $i$-th bit (in binary), then $x\,|\,y$ has a 1 in the $i$-th bit.
• If both $x$ and $y$ have a 0 in the $i$-th bit (in binary), then $x\,|\,y$ has a 0 in the $i$-th bit.

Examples of computing the bitwise OR of two integers:

• $2\,|\,4=010_2\,|\,100_2=110_2=6$
• $3\,|\,6=011_2\,|\,110_2=111_2=7$
• $5\,|\,4=101_2\,|\,100_2=101_2=5$

Non-negative integers $l$, $r$, and $x$ are given, with $l \le r$. You must find the value of the following expression.

$\text{mex}([(l\,|\,x),((l+1)\,|\,x),\cdots,((r-1)\,|\,x),(r\,|\,x)])$

Three integers $l$, $r$, and $x$ are given on one line, separated by spaces. ($0 \le l \le r \le 1\,000$, $0 \le x \le 1\,000$)

Print the answer to the problem on one line.

In most languages, the bitwise OR $x\,|\,y$ of non-negative integers $x$ and $y$ can be computed with the operator |, as in (x|y).