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: $011 \oplus 101 = 110)$.
  

Input

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

Output

Print the answer.

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.

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

见题面 Input 部分

见题面 Output 部分