CF1056B.Divide Candies

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.

阿尔卡季和他的朋友们喜欢在一个 $n \times n$ 的棋盘上玩国际跳棋。棋盘的行和列均从 $1$ 编号至 $n$。

朋友们最近赢得了一项锦标赛冠军，因此阿尔卡季想用一些糖果来犒劳他们。他想起一则古老的寓言（但不记得其寓意），于是决定为棋盘上的每个格子准备一份糖果：格子 $(i, j)$ 对应的糖果包中恰好包含 $i^2 + j^2$ 颗独一无二种类的糖果。

共有 $m$ 位朋友理应获得这份礼物。在这 $n \times n$ 份糖果包中，有多少份可以被均等地分成 $m$ 份，且不允许将任何一颗糖果切开？注意：每份糖果包必须独立分割，因为不同格子中的糖果种类互不相同。

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.

唯一的一行包含两个整数 $n$ 和 $m$（$1 \le n \le 10^9$，$1 \le m \le 1000$）——分别为场地的大小以及将集合划分成的部分数。

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

输出一个整数——可以被均等划分的集合的数量。

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 $m = 1$.

在第一个例子中，只有单元格 $(3, 3)$ 对应的集合可以被均分（$3^2 + 3^2 = 18$，可被 $m=3$ 整除）。

在第二个例子中，以下单元格对应的集合可以被均分：

• $(1, 2)$ 和 $(2, 1)$，因为 $1^2 + 2^2 = 5$，可被 $5$ 整除；
• $(1, 3)$ 和 $(3, 1)$；
• $(2, 4)$ 和 $(4, 2)$；
• $(2, 6)$ 和 $(6, 2)$；
• $(3, 4)$ 和 $(4, 3)$；
• $(3, 6)$ 和 $(6, 3)$；
• $(5, 5)$。

在第三个例子中，所有单元格对应的集合均可被均分，因为 $m = 1$。