How many ways?

Write a program which identifies the number of combinations of three integers which satisfy the following conditions:

• You should select three distinct integers from 1 to n.
• A total sum of the three integers is x.

For example, there are two combinations for n = 5 and x = 9.

• 1 + 3 + 5 = 9
• 2 + 3 + 4 = 9

Note

解説

Constraints

• 3 ≤ n ≤ 100
• 0 ≤ x ≤ 300

Input

The input consists of multiple datasets. For each dataset, two integers n and x are given in a line.

The input ends with two zeros for n and x respectively. Your program should not process for these terminal symbols.

Output

For each dataset, print the number of combinations in a line.

Example

Input

5 9 0 0

Output

2

inputFormat

Input

The input consists of multiple datasets. For each dataset, two integers n and x are given in a line.

The input ends with two zeros for n and x respectively. Your program should not process for these terminal symbols.

outputFormat

Output

For each dataset, print the number of combinations in a line.

Example

Input

5 9 0 0

Output

2

样例

5 9
0 0

2