Description

There are $n$ functions, denoted as $F_1, F_2, ..., F_n$. Each function is defined as $F_i(x) = A_i x^2 + B_i x + C_i$ where $x \in \mathbb{N}^*$.
Given the coefficients $A_i$, $B_i$, and $C_i$ for each function, determine the smallest $m$ function values among all possible values generated by these functions (if there are duplicates, output them multiple times).

Input Format

The first line contains two positive integers $n$ and $m$.
Each of the following $n$ lines contains three positive integers representing the coefficients $A_i$, $B_i$, and $C_i$ for the $i$-th function. It is guaranteed that $A_i \leq 10$, $B_i \leq 100$, and $C_i \leq 10000$.

Output Format

Output the first $m$ smallest function values from the sorted list of all possible values generated by these $n$ functions. The $m$ numbers should be printed on a single line, separated by spaces.

3 10
4 5 3
3 4 5
1 7 1

9 12 12 19 25 29 31 44 45 54

Hint

【Data Scale】 $n, m \leq 10000$.