Itami has bought pieces of candy, and would like to share them with his friends.

However, they are very picky about the amount of candies that they eat. Lelei only wants a **prime number** of candies, Rory wants candies in multiples of , her favorite number, and Tuka, trying to keep a slim and trim figure, will take **at most** candy.

In how many different ways can Itami distribute his bag of candies? A distribution is considered different if at least one of his friends gets a different amount of candy. Note that Itami does not have to distribute all candies; he can choose to eat any remainders by himself.

#### Note

A **prime number** is a positive integer greater than that has no other factors other than and itself.

A **multiple** of a number is any number such that is an integer.

#### Input Specification

The first line of input will contain two space-separated integers , the number of candies Itami has, and , Rory's favorite number.

#### Output Specification

A single integer, the number of ways Itami can hand out his candies.

#### Sample Input 1

`3 1`

#### Sample Output 1

`4`

#### Explanation for Sample Output 1

The ways of distributing are, in order of : , , , .

#### Sample Input 2

`1 1`

#### Sample Output 2

`0`

#### Explanation for Sample Output 2

Lelei must take at least candies, but Itami doesn't have that many to give. Thus, there is no way to distribute candies.

#### Sample Input 3

`10 3`

#### Sample Output 3

`19`

## Comments

I am having difficulty in finding the errors in my code. It works fine with sample inputs, but not some batches. Why?

Hi All,

I have tested my code with all the test cases and it seems to be working fine. However, it is very inconsistent within the batches.It would be great if someone can offer a hint.

Thanks!

I think you forgot to take into consideration the case where there is not enough candy left to give to Tuka.

I included the two cases: one Tuka takes one candy, and the other one he does not. Are you sure that is the problem? Thanks!

Multiples can't be negative right?

Each person must get zero or more candies.

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No comment. Read the task description again.

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