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- Project Euler #239: Twenty-two Foolish Primes

# Project Euler #239: Twenty-two Foolish Primes

# Project Euler #239: Twenty-two Foolish Primes

_{This problem is a programming version of Problem 239 from projecteuler.net}

A set of disks numbered through are placed in a line in random order.

What is the probability that we have a partial derangement such that exactly prime number discs are found away from their natural positions? (Any number of non-prime disks may also be found in or out of their natural positions.)

It can be shown that for a given constraints the answer can be represented as , where and are coprime positive integers and . Print the value of modulo .

**Input Format**

The only line of input contains two integers and separated by single space.

**Constraints**

- where is number of primes in range from to inclusive.

**Output Format**

Print the only line with the answer.

**Sample Input 0**

```
10 3
```

**Sample Output 0**

```
498412760
```

**Explanation 0**

The actual value of is .