Sticks box

The box contains $N$ sticks, which need to be divided between friends Renato, Gustavo and Bruno, for a school job. Each friend must earn at least 1 (one) toothpick. The teacher will determine the maximum number of $M$ sticks that each one can earn.

In this task, given $N$ and $M$, your program must calculate how many different ways there are to divide all $N$ sticks among the three friends. For example, for $N = 100$; if $M = 15$, then there are zero ways of dividing because the sum of the numbers of Renato, Gustavo and Bruno's toothpicks would be at most 45, only it must always be $N$; but if $M = 34$, then there would be six different ways:

Input

The entry consists of only one line with two natural numbers $N$ and $M$, indicating respectively the number of sticks in the box and the maximum amount that each friend can win.

Output

Your program should write a single line in the output, containing a single integer: how many different ways are there to divide $N$ sticks among the three friends.

Constraints

• $3 \leq N \leq 100000$
• $1 \leq M \leq N$