Problem statement

Given the integers $ N $ and $ X $. Find the remainder by dividing the number of sequences of length $ N $ that satisfy the following conditions by $ 998244353 $.

• The sequence is a monotonous increase in a broad sense.
• Each element of the sequence is greater than or equal to $ 0 $ and less than or equal to $ X $.
• The exclusive OR (xor) of all elements is $ X $.

Constraint

• $1 \ leq N \ leq 500$
• $0 \ leq X \ leq 500$
• $ N $ and $ X $ are integers.

input

Input is given from standard input in the following format.

$ N $ $ X $

output

Output the answer.

Input example 1

twenty three

Output example 1

2

The sequences $\\ {0,3 \\}$ and $\\ {1,2 \\}$ satisfy the condition.

Input example 2

1 1

Output example 2

1

Only the sequence $\\ {1 \\}$ meets the condition.

Input example 3

224 239

Output example 3

400351036

Example

Input

2 3

Output

2

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