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.

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