For an array of integers $a$, let's define $|a|$ as the number of elements in it.

Let's denote two functions:

• $F(a, k)$ is a function that takes an array of integers $a$ and a positive integer $k$. The result of this function is the array containing $|a|$ first elements of the array that you get by replacing each element of $a$ with exactly $k$ copies of that element.

  For example, $F([2, 2, 1, 3, 5, 6, 8], 2)$ is calculated as follows: first, you replace each element of the array with $2$ copies of it, so you obtain $[2, 2, 2, 2, 1, 1, 3, 3, 5, 5, 6, 6, 8, 8]$. Then, you take the first $7$ elements of the array you obtained, so the result of the function is $[2, 2, 2, 2, 1, 1, 3]$.

• $G(a, x, y)$ is a function that takes an array of integers $a$ and two different integers $x$ and $y$. The result of this function is the array $a$ with every element equal to $x$ replaced by $y$, and every element equal to $y$ replaced by $x$.

  For example, $G([1, 1, 2, 3, 5], 3, 1) = [3, 3, 2, 1, 5]$.

An array $a$ is a parent of the array $b$ if:

• either there exists a positive integer $k$ such that $F(a, k) = b$;
• or there exist two different integers $x$ and $y$ such that $G(a, x, y) = b$.

An array $a$ is an ancestor of the array $b$ if there exists a finite sequence of arrays $c_0, c_1, \dots, c_m$ ($m \ge 0$) such that $c_0$ is $a$, $c_m$ is $b$, and for every $i \in [1, m]$, $c_{i-1}$ is a parent of $c_i$.

And now, the problem itself.

You are given two integers $n$ and $k$. Your goal is to construct a sequence of arrays $s_1, s_2, \dots, s_m$ in such a way that:

• every array $s_i$ contains exactly $n$ elements, and all elements are integers from $1$ to $k$;
• for every array $a$ consisting of exactly $n$ integers from $1$ to $k$, the sequence contains at least one array $s_i$ such that $s_i$ is an ancestor of $a$.

Print the minimum number of arrays in such sequence.