Jõululaul

Time limit1sMemory limit1024 MB

Summary

Given N, print for each k from 1 to N the total count of gift A_k, which is k times (N minus k plus 1).

Level: Easy1 of 10
Topics: Math, Implementation
Solved: No attempts yet

The Twelve Days of Christmas

On the second Advent today, we recall an English Christmas carol that is about 200 years old:

On the first day of Christmas, my true love sent to me one partridge in a pear tree.

On the second day of Christmas, my true love sent to me two turtle doves and a partridge in a pear tree.

On the third day of Christmas, my true love sent to me three French hens, two turtle doves and a partridge in a pear tree.

On the fourth day of Christmas, my true love sent to me four calling birds, three French hens, two turtle doves and a partridge in a pear tree.

In the magic land of programming exercises, Christmas lasts $N$ days, and there are $N$ different gifts, denoted $A_1$ , $A_2$ , $\ldots$ , $A_N$ . On day $k$ of Christmas, my true love sends me one $A_1$ , two $A_2$ , three $A_3$ , $\dots$ , and $k$ of $A_k$ .

Write a program that finds how many gifts of each kind my true love sends me in total.

Input

A single line contains an integer $N$ , the number of days Christmas lasts in the magic land ( $1 \le N \le 100\,000$ ).

Output

Print exactly $N$ lines, one integer per line. On line $k$ , print the total number of $A_k$ gifts received during the holiday.

Examples2

Example 1
Input
```
2
```
Expected output
```
2
2
```
Example 2
Input
```
5
```
Expected output
```
5
8
9
8
5
```