Note

The execution time limit for this problem is 3500[ms].

Problem Statement

You are given as input a positive integer $B$ and a positive integer $C$ that is a divisor of $B$.

Define an undirected graph $G_{B,C} = (V_{B,C},E_{B,C})$ with infinitely many vertices and infinitely many edges, having no self-loops or multiple edges, as follows:

• The vertex set $V_{B,C}$ of $G_{B,C}$ is the set of all square matrices of order $2$ with integer coefficients $\displaystyle \left( \begin{array}{cc} a & b \\ c & d \end{array} \right) $ that satisfy all of the following $4$ conditions.
• $a$ is coprime to $B$ (that is, no prime number divides both).
• $b \equiv 0 \pmod{C}$.
• $c \equiv 0 \pmod{B}$.
• $d \equiv 1 \pmod{B}$.
• The edge set $E_{B,C}$ of $G_{B,C}$ is the set of all edges $\{P,Q\}$ connecting $2$ distinct points $P,Q$ of $V_{B,C}$ that satisfy the following condition.
  • There exists a point $R$ of $V_{B,C}$ that satisfies at least one of the following $2$ conditions.
  • Every entry of $PR - RQ$ is a multiple of $B$.
  • Every entry of $QR - RP$ is a multiple of $B$.

Then, as non-trivial facts,

• $G_{B,C}$ has only finitely many connected components, and
• each connected component of $G_{B,C}$ is a complete graph,

can both be proved. Determine whether the number of connected components of $G_{B,C}$ is greater than $100$, and if it is at most $100$, also find its value.

Background

This section explains the background for those familiar with group theory. First, let $\overline{G}_{B,C}$ be the set of all invertible square matrices of order $2$ with coefficients in $\mathbb{Z}/B \mathbb{Z}$ whose $(1,2)$ entry is a multiple of $C + B \mathbb{Z}$ and whose row $2$ is $(0 + B \mathbb{Z},1 + B \mathbb{Z})$. Then $\overline{G}_{B,C}$ forms a group under matrix multiplication.

Furthermore, for any vertex $P$ of $G_{B,C}$, taking the remainder of each entry of $P$ modulo $B$ gives an element $\overline{P}$ of $\overline{G}_{B,C}$. This correspondence defines a map $G_{B,C} \to \overline{G}_{B,C}$. In fact, a subset $S$ of $G_{B,C}$ is connected if and only if any $2$ elements of the image of $S$ under this map are conjugate in the group $\overline{G}_{B,C}$.

In other words, this problem is equivalent to determining whether the total number of conjugacy classes of the group $\overline{G}_{B,C}$ is greater than $100$, and finding the total number of conjugacy classes if it is at most $100$. It is known that the total number of conjugacy classes of a finite group corresponds to the count of isomorphism classes of complex irreducible representations, which makes it a very important value in representation theory.

Input

The input is given from standard input on $1$ line in the following format:

$B$ $C$

• Line $1$ contains $B,C$ separated by a half-width space.

Constraints

The input satisfies the following constraints:

• $B$ is an integer satisfying $1 \leq B \leq 6 \times 10^2$.
• $C$ is a divisor of $B$ satisfying $1 \leq C \leq B$.

Output

If the number of connected components of $G_{B,C}$ is greater than $100$, print 100+; if it is at most $100$, print that value on $1$ line.

Print a newline at the end.

Sample

1 1

1

3 3

2

24 2

30

80 2

100+