Minimum Function Value

Problem Background

Special for beginners, ^_^

Problem Description

There are $n$ functions $F_1, F_2, \dots, F_n$. They are defined as $F_i(x) = A_i x^2 + B_i x + C_i$ ($x \in N^*$). Given $A_i, B_i, C_i$, find the smallest $m$ values among all the function values produced by all the functions (output a value as many times as it occurs if there are duplicates).

Input Format

The first line contains two positive integers $n$ and $m$.

The following $n$ lines each contain three positive integers: the $i$-th line gives $A_i$, $B_i$ and $C_i$. The input guarantees $A_i \le 10$, $B_i \le 100$, $C_i \le 10000$.

Output Format

Output the first $m$ elements after sorting all the function values that can be generated by the $n$ functions. These $m$ numbers should be printed on one line, separated by spaces.

Sample Input

3 10
4 5 3
3 4 5
1 7 1

Sample Output

9 12 12 19 25 29 31 44 45 54

Constraints

Time limit: 1s; memory limit: 1024 KiB for each test case. $n, m \le 10000$.