SGU - 403 - Scientific Problem （水）

403. Scientific Problem

Time limit per test: 0.25 second(s)

Memory limit: 65536 kilobytes

input: standard

output: standard

Once upon a time Professor Idioticideasinventor was travelling by train. Watching cheerless landscape outside the window, he decided to invent the theme of his new scientific work. All of a sudden a brilliant idea struck him: to develop an effective algorithm
finding an integer number, which is x times less than the sum of all its integer positive predecessors, where number x is given. As far as he has no computer in the train, you have to solve this difficult problem.

Input

The first line of the input file contains an integer number x (1 ≤ x ≤ 10⁹).

Output

Output an integer number — the answer to the problem.

Example(s)

sample input	sample output
1	3

sample input	sample output
2	5

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思路：先给出一个数x。求出数n，使得n是n之前全部数(不包含n)的总和的1/x

由求和公式n*(n-1)/2/x = n 可得 n=2*x+1

AC代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

int main() {
	int x;
	while(scanf("%d", &x) != EOF) {
		printf("%d\n", 2*x+1);
	}
	return 0;
}