Problem Statement

Given are integers $L$, $R$, and $V$. Find the number of pairs of integers $(l,r)$ that satisfy both of the conditions below, modulo $998244353$.

• $L \leq l \leq r \leq R$
• $l \oplus (l+1) \oplus \cdots \oplus r=V$

Here, $\oplus$ denotes the bitwise $\mathrm{XOR}$ operation.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$.

Constraints

• $1 \leq L \leq R \leq 10^{18}$
• $0 \leq V \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

L R V

Output

Print the answer.