Problem Statement

Print the number of integer sequences of length $N$, $A = (A_1, A_2, \\ldots, A_N)$, that satisfy both of the following conditions, modulo $998244353$.

• $0 \\leq A_1 \\leq A_2 \\leq \\cdots \\leq A_N \\leq M$
• $A_1 \\oplus A_2 \\oplus \\cdots \\oplus A_N = X$

Here, $\\oplus$ denotes bitwise XOR.

What is bitwise XOR?

The bitwise XOR of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows.

• When $A \\oplus B$ is written in binary, the $k$-th lowest bit ($k \\geq 0$) is $1$ if exactly one of the $k$-th lowest bits of $A$ and $B$ is $1$, and $0$ otherwise.

For instance, $3 \\oplus 5 = 6$ (in binary: $011 \\oplus 101 = 110$).

Constraints

• $1 \\leq N \\leq 200$
• $0 \\leq M \\lt 2^{30}$
• $0 \\leq X \\lt 2^{30}$
• All values in the input are integers.

Input

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

$N$ $M$ $X$

Output

Print the answer.

Sample Input 1

3 3 2

Sample Output 1

5

Here are the five sequences of length $N$ that satisfy both conditions in the statement: $(0, 0, 2), (0, 1, 3), (1, 1, 2), (2, 2, 2), (2, 3, 3)$.

Sample Input 2

200 900606388 317329110

Sample Output 2

788002104