Count Perfect Square Sums in Consecutive Numbers

Given two integers (n) and (k), determine the number of sequences of (k) consecutive numbers taken from (1) to (n) whose sum is a perfect square.

For a starting index (i) (where (1 \le i \le n-k+1)), the sum of the consecutive sequence is given by:
[ S = k \cdot i + \frac{k(k-1)}{2} ]
A sum (S) is a perfect square if there exists an integer (m) such that (S = m^2).

inputFormat

Input consists of a single line containing two space-separated integers: (n) and (k).

outputFormat

Output a single integer representing the count of (k)-length consecutive segments from (1) to (n) whose sum is a perfect square.

sample

10 2

1