Problem Statement

How many different sequences of length $2N, A = (A_1, A_2, \dots, A_{2N}),$ satisfy both of the following conditions?

• The sequence A contains N occurrences of +1 and N occurrences of -1.
• There are exactly K pairs of l and $r (1 \leq l \leq r \leq 2N)$ such that $A_l + A_{l+1} + \cdots + A_r = 0$.

Input

Input is given from Standard Input in the following format:
N K

Output

Print the number of different sequences that satisfy the conditions in Problem Statement.
The answer always fits into the signed 64-bit integer type.

Constraints

• $1 \leq N \leq 30$
• $1 \leq K \leq N^2$
• All values in input are integers.

Sample Input 1

1 1

Sample Output 1

2

For N = 1, K = 1, two sequences below satisfy the conditions:

• A = (+1, -1)
• A = (-1, +1)

Sample Input 2

2 3

Sample Output 2

2

For N = 2, K = 3, two sequences below satisfy the conditions:

• A = (+1, -1, -1, +1)
• A = (-1, +1, +1, -1)

Sample Input 3

3 7

Sample Output 3

6

For N = 3, K = 7, six sequences below satisfy the conditions:

• A = (+1, -1, +1, -1, -1, +1)
• A = (+1, -1, -1, +1, +1, -1)
• A = (+1, -1, -1, +1, -1, +1)
• A = (-1, +1, +1, -1, +1, -1)
• A = (-1, +1, +1, -1, -1, +1)
• A = (-1, +1, -1, +1, +1, -1)

Sample Input 4

8 24

Sample Output 4

568

Sample Input 5

30 230

Sample Output 5

761128315856702

Sample Input 6

25 455

Sample Output 6

0

For N = 25, K = 455, no sequences satisfy the conditions.

见题面 Input 部分

见题面 Output 部分