Description

Define the function $f(\prod p_i^{a_i})=\sum a_ip_i$, where $p_i$ are primes. In particular, $f(1)=0$.

For $k\in\{0,1\}$, define the function $g$ as:

Given $m$ and $k$, for all $1\le i\le\lfloor\sqrt m\rfloor$, compute $g(\lfloor\frac mi\rfloor,k,r)$ for all $0\le r<4$.

Input Format

The first line contains a positive integer $m$.
The second line contains a non-negative integer $k$.

Output Format

Output $\lfloor\sqrt m\rfloor$ lines.
The $i$-th line contains four non-negative integers, and the $r$-th non-negative integer is $g(\lfloor\frac mi\rfloor,k,r)$.

10 0

2 2 3 3
2 1 1 1
1 0 1 1

Hint

Explanation of Sample 1

$f=[0,2,3,0,1,1,3,2,2,3,\dots]$

Constraints

This problem uses bundled testdata.

For $100\%$ of the testdata, $1\le m\le10^{10}$ and $0\le k\le1$.

Translated by ChatGPT 5