Farmer John's farm is full of lush vegetation and every cow wants a photo of its natural beauty. Unfortunately, Bessie still has places to be, but she doesn't want to disrupt any photo ops.

Bessie is currently standing at $(X,0)$ on the XY-plane and she wants to get to $(0,Y)$ ($1\le X,Y\le 10^6$). Unfortunately, $N$ ($1 \leq N \leq 3 \cdot 10^5$) other cows have decided to pose on the $X$ axis. More specifically, cow $i$ will be positioned at $(x_i,0)$ with a photographer at $(0,y_i)$ where $(1 \leq x_i,y_i \leq 10^6)$ ready to take their picture. They will begin posing moments before time $s_i$ ($1 \leq s_i < T$) and they will keep posing for a very long time (they have to get their picture just right). Here, $1\le T\le N+1$.

Bessie knows the schedule for every cow's photo op, and she will take the shortest Euclidean distance to get to her destination, without crossing the line of sight from any photographer to their respective cow (her path will consist of one or more line segments).

If Bessie leaves at time $t$, she will avoid the line of sights for all photographer/cow pairs that started posing at time $s_i \le t$, and let the distance to her final destination be $d_t$. Determine the values of $\lfloor d_t\rfloor$ for each integer $t$ from $0$ to $T-1$ inclusive.

SAMPLE INPUT:

4 5
6 7
1 7 5
2 4 4
3 1 6
4 2 9

SAMPLE OUTPUT:

9
9
9
10
12

SAMPLE INPUT:

2 3
10 7
1 2 10
1 9 1

SAMPLE OUTPUT:

12
16
16

For $t=0$ the answer is $\lfloor \sqrt{149} \rfloor=12$.

For $t=1$ the answer is $\lfloor 14+\sqrt 5\rfloor=16$.

SAMPLE INPUT:

5 6
8 9
1 3 5
1 4 1
3 10 7
4 9 2
5 6 6

SAMPLE OUTPUT:

12
12
12
12
14
14

For $t=5$ the answer is $\lfloor 1+\sqrt{9^2+7^2}+2\rfloor=14$. Path: $(8,0)\to (9,0)\to (0,7)\to (0,9)$

Problem credits: Suhas Nagar