Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

B. Divide Candies
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Arkady and his friends love playing checkers on an $$$n \times n$$$ field. The rows and the columns of the field are enumerated from $$$1$$$ to $$$n$$$.

The friends have recently won a championship, so Arkady wants to please them with some candies. Remembering an old parable (but not its moral), Arkady wants to give to his friends one set of candies per each cell of the field: the set of candies for cell $$$(i, j)$$$ will have exactly $$$(i^2 + j^2)$$$ candies of unique type.

There are $$$m$$$ friends who deserve the present. How many of these $$$n \times n$$$ sets of candies can be split equally into $$$m$$$ parts without cutting a candy into pieces? Note that each set has to be split independently since the types of candies in different sets are different.

Input

The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^9$$$, $$$1 \le m \le 1000$$$) — the size of the field and the number of parts to split the sets into.

Output

Print a single integer — the number of sets that can be split equally.

Examples
Input
3 3
Output
1
Input
6 5
Output
13
Input
1000000000 1
Output
1000000000000000000
Note

In the first example, only the set for cell $$$(3, 3)$$$ can be split equally ($$$3^2 + 3^2 = 18$$$, which is divisible by $$$m=3$$$).

In the second example, the sets for the following cells can be divided equally:

  • $$$(1, 2)$$$ and $$$(2, 1)$$$, since $$$1^2 + 2^2 = 5$$$, which is divisible by $$$5$$$;
  • $$$(1, 3)$$$ and $$$(3, 1)$$$;
  • $$$(2, 4)$$$ and $$$(4, 2)$$$;
  • $$$(2, 6)$$$ and $$$(6, 2)$$$;
  • $$$(3, 4)$$$ and $$$(4, 3)$$$;
  • $$$(3, 6)$$$ and $$$(6, 3)$$$;
  • $$$(5, 5)$$$.

In the third example, sets in all cells can be divided equally, since $$$m = 1$$$.