Combination of Number Sequences

Consider a sequence of n numbers using integers from 0 to 9 k1, k2, ..., kn. Read the positive integers n and s,

k1 + 2 x k2 + 3 x k3 + ... + n x kn = s

Create a program that outputs how many rows of n numbers such as. However, the same number does not appear more than once in one "n sequence of numbers".

Input

The input consists of multiple datasets. For each dataset, n (1 ≤ n ≤ 10) and s (0 ≤ s ≤ 10,000) are given on one line, separated by blanks.

The number of datasets does not exceed 100.

Output

For each dataset, print the number of combinations in which the sum of n integers is s on one line.

Example

Input

3 10 3 1

Output

8 0

inputFormat

outputFormat

outputs how many rows of n numbers such as. However, the same number does not appear more than once in one "n sequence of numbers".

Input

The input consists of multiple datasets. For each dataset, n (1 ≤ n ≤ 10) and s (0 ≤ s ≤ 10,000) are given on one line, separated by blanks.

The number of datasets does not exceed 100.

Output

For each dataset, print the number of combinations in which the sum of n integers is s on one line.

Example

Input

3 10 3 1

Output

8 0

样例

3 10
3 1

8
0

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