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data structures

math

*2300

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F. Pairwise Modulo

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have an array $$$a$$$ consisting of $$$n$$$ distinct positive integers, numbered from $$$1$$$ to $$$n$$$. Define $$$p_k$$$ as $$$$$$p_k = \sum_{1 \le i, j \le k} a_i \bmod a_j,$$$$$$ where $$$x \bmod y$$$ denotes the remainder when $$$x$$$ is divided by $$$y$$$. You have to find and print $$$p_1, p_2, \ldots, p_n$$$.

Input

The first line contains $$$n$$$ — the length of the array ($$$2 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ space-separated distinct integers $$$a_1, \ldots, a_n$$$ ($$$1 \le a_i \le 3 \cdot 10^5$$$, $$$a_i \neq a_j$$$ if $$$i \neq j$$$).

Output

Print $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$.

Examples

Input

4 6 2 7 3

Output

0 2 12 22

Input

3 3 2 1

Output

0 3 5

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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