A12928 | p-binary

Vasya will fancy any number as long as it is an integer power of two. Petya, on the other hand, is very conservative and only likes a single integer $p$ (which may be positive, negative, or zero). To combine their tastes, they invented $p$ -binary numbers of the form $2^x + p$ , where $x$ is a non-negative integer.

For example, some $-9$ -binary ("minus nine" binary) numbers are: $-8$ (minus eight), $7$ and $1015$ ( $-8=2^0-9$ , $7=2^4-9$ , $1015=2^{10}-9$ ).

The boys now use $p$ -binary numbers to represent everything. They now face a problem: given a positive integer $n$ , what's the smallest number of $p$ -binary numbers (not necessarily distinct) they need to represent $n$ as their sum? It may be possible that representation is impossible altogether. Help them solve this problem.

For example, if $p=0$ we can represent $7$ as $2^0 + 2^1 + 2^2$ .

And if $p=-9$ we can represent $7$ as one number $(2^4-9)$ .

Note that negative $p$ -binary numbers are allowed to be in the sum (see the Notes section for an example).

The only line contains two integers $n$ and $p$ ( $1 \leq n \leq 10^9$ , $-1000 \leq p \leq 1000$ ).

If it is impossible to represent $n$ as the sum of any number of $p$ -binary numbers, print a single integer $-1$ . Otherwise, print the smallest possible number of summands.