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 .
The only line of input contains two integers and separated by single space.
where is number of primes in range from to inclusive.