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 $p_1, p_2, p_3, \dots p_k$.
  

Input

Input is given from Standard Input in the following format:
L R V

Output

Print the answer.

Constraints

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

Sample Input 1

1 3 3

Sample Output 1

2

The two pairs satisfying the conditions are (l,r)=(1,2) and (l,r)=(3,3).

Sample Input 2

10 20 0

Sample Output 2

6

Sample Input 3

1 1 1

Sample Output 3

1

Sample Input 4

12345 56789 34567

Sample Output 4

16950

见题面 Input 部分

见题面 Output 部分