Prime Cuts

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Problem

A prime number is a counting number ($1, 2, 3, \ldots$) that is evenly divisible only by $1$ and itself; in this problem the value $1$ is also included in the prime list. Given an integer $N$, build the ordered list of prime numbers from $1$ to $N$ (inclusive). Then cut some primes from the center of this list: if the list holds an even number of primes, print $C \times 2$ primes from the center; if it holds an odd number of primes, print $(C \times 2) - 1$ primes from the center.

Input

Each input set is on a line by itself and consists of two integers. The first number $N$ ($1 \le N \le 1000$) is the maximum value of the range used to build the prime list (that is, primes from $1$ to $N$). The second number $C$ ($1 \le C \le N$) defines how many center primes to print: $C \times 2$ when the list length is even, or $(C \times 2) - 1$ when the list length is odd. Input continues until the end of the file.

Output

For each input set, print $N$ starting in the first column, followed by a space, then $C$, then a colon (:), and then the center primes defined above. Each center prime must be preceded by exactly one space. If the number of center primes to cut exceeds the size of the prime list from $1$ to $N$, print the entire list instead. Separate the outputs of consecutive input sets with a single blank line.