Description

There are $n$ functions, denoted $F_1, F_2, \dots, F_n$. Define $F_i(x) = A_i x^2 + B_i x + C_i$ for $x \in \mathbb{N}^*$. Given these $A_i$, $B_i$, and $C_i$, find the smallest $m$ values among all function values of all 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 integers; on the $i$-th line they are $A_i$, $B_i$, and $C_i$.

Output Format

Output the first $m$ elements of the sorted sequence of all function values generated by the $n$ functions. Print these $m$ numbers on one 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

Constraints

For all test points, it is guaranteed that $1 \leq n, m \leq 10000$, $1 \leq A_i \leq 10$, $0 \leq B_i \leq 100$, $0 \leq C_i \leq 10^4$.

Translated by ChatGPT 5