Xor Array

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

inputFormat

input

Input is given from standard input in the following format.

$N$ $X$

outputFormat

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

样例

2 3

2