Ohani was tired of sitting in a mall, watching people hold hands. He hates public displays of affection (PDA). So, he decided to take a walk. He was walking through a magical forest when he came across a porcupine. He noticed that the porcupine's body was completely made of gold. The porcupine said:

Over a period of $T$ seconds, I will shoot $N$ quills out in total. The $i^{th}$ quill exists only between the $L_i^{th}$ and $R_i^{th}$ seconds (inclusive).

The height of the $i^{th}$ can be expressed as $a_i{x}^2+b_{i}x+c_i$, where $a_i$, $b_i$, and $c_i$ are constants for the $i^{th}$ quill and $x$ is the number of seconds the quill has been in the air. For the $i^{th}$ quill, at time $L_i$, $x=0$.

These quills have magical gravity and pass through anything, so it's perfectly fine for $a_i$ to be more than $0$ or the height of a quill to be less than $0$ at any point in time.

Can you tell me the sum of the heights of all the quills at each second in time between $1$ and $T$ inclusive?

Ohani was able to solve the problem and get home just in time to play with legos with his brother. Ohani loves legos, and his brother is a lego lover too.

Input Specification

The first line will contain two integers, $N,T$ $(1\le N\le {10}^5,1\le T\le {10}^5)$.

The next $N$ lines will each contain five integers, $L_i,R_i,a_i,b_i,c_i$ $(1\le L_i\le R_i\le T,0\le |a_i|,|b_i|,|c_i|\le {10}^3)$.

Output Specification

Print $T$ integers on one line, the $t^{th}$ integer representing the sum of heights of quills at the $t^{th}$ $(1\le t\le T)$ second in time.

Constraints

Subtask 1 [1%]

$T=1$

Subtask 2 [4%]

$N,T\le 1000$

Subtask 3 [5%]

$L_i=1,R_i=T$

Subtask 4 [20%]

$a_i=1,b_i=1$

Subtask 5 [70%]

No additional constraints.

Sample Input

2 6
1 6 1 3 2
3 4 2 2 -200

Sample Output

2 6 -188 -176 30 42

Explanation of Sample Output

The first quill's trajectory is shown as follows:

The second quill's trajectory is shown as follows:

At the $1^{st}$ second, the sum of the heights is only quill $1$ at $x=0$ as quill $2$ does not exist yet $(2)$.

At the $2^{nd}$ second, the sum of the heights is only quill $1$ at $x=1$ as quill $2$ does not exist yet $(6)$.

At the $3^{rd}$ second, the sum of the heights is quill $1$ at $x=2$ and quill $2$ at $x=0$ $(12+(-200)=-188)$.

At the $4^{th}$ second, the sum of the heights is quill $1$ at $x=3$ and quill $2$ at $x=1$ $(20+(-196)=-176)$.

At the $5^{th}$ second, the sum of the heights is only quill $1$ at $x=4$ as quill $2$ no longer exists $(30)$.

At the $6^{th}$ second, the sum of the heights is only quill $1$ at $x=5$ as quill $2$ no longer exists $(42)$.