Description

Under Flandre's guidance, Koishi has become a math master, and she came up with a simple math problem.

Given an integer $n$, let $\displaystyle f(x) = \sum_{i=1}^n x \bmod i$. You need to output $f(1), f(2), \ldots, f(n)$.

As usual, Koishi pretends she cannot solve this problem and asks you for help.

Input Format

A positive integer $n$.

Output Format

One line containing $n$ integers $f(1), f(2), \ldots, f(n)$ separated by spaces.

10

9 16 22 25 29 27 29 24 21 13

Hint

For $20\%$ of the testdata, $n \le 1000$.
For $60\%$ of the testdata, $n \le 10^5$.
For $100\%$ of the testdata, $1 \le n \le 10^6$.

Translated by ChatGPT 5