Given a positive integer N and a common difference k$,$ determine the number of arithmetic progressions consisting of integers with a common difference of k$,$ such that their sum is equal to N$.$

Input

The only line of the input contains $2$ integers N and k$.$

Constraints:

N QUESTION

Progression Count $($CodeRush January'$24)$

Time Limit: $2,$ Memory Limit: $128000$

Given a positive integer $N$ and a common difference $k,$ determine the number of arithmetic progressions consisting of integers with a common difference of $k,$ such that their sum is

equal to $N.$

Input

The only line of the input contains $2$ integers $N$ and $k.$

Constraints:

$1N{10}^9$

$1k1000000$

Output

Output a single integer, the number of such arithmetic progressions consisting of integers.

Example

Input:

$61$

Output:

$49$

k

Output

Output a single integer, the number of such arithmetic progressions consisting of integers.

Example

Input:

$61$

Output:

$4$

AP's : $\{1,2,3\},\{0,1,2,3\},\{6\},\{-5,-4,-3...3,4,5,6\}.$

Input:

$93$

Output:

$6$