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 .