p-binary

2000ms

524288K

Description:

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).

Input:

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

Output:

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.

Sample Input:

24 0

Sample Output:

Sample Input:

24 1

Sample Output:

Sample Input:

24 -1

Sample Output:

Sample Input:

4 -7

Sample Output:

Sample Input:

1 1

Sample Output:

-1

Note:

$$$0$$$-binary numbers are just regular binary powers, thus in the first sample case we can represent $$$24 = (2^4 + 0) + (2^3 + 0)$$$.

In the second sample case, we can represent $$$24 = (2^4 + 1) + (2^2 + 1) + (2^0 + 1)$$$.

In the third sample case, we can represent $$$24 = (2^4 - 1) + (2^2 - 1) + (2^2 - 1) + (2^2 - 1)$$$. Note that repeated summands are allowed.

In the fourth sample case, we can represent $$$4 = (2^4 - 7) + (2^1 - 7)$$$. Note that the second summand is negative, which is allowed.

In the fifth sample case, no representation is possible.

Informação

Provedor Codeforces

Código CF1225C