Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>

#define GM(a) (a*(a+1)/2)

int X;

int jump(){
	for( int i = 0; i < X; i++ ){
		if( GM(i) >= X ){ return i; }
	}
	return -1;
}

int main(){
	std::cin >> X;
	std::cout << jump() << std::endl;
	return 0;
}

/*
int jump(int x, int i, int M){
	int re = -1;
	std::cout << x << "," << i << "," << M << std::endl;
	if( x == X ){ return i-1; }
	if( i > M ){ return -1; }
	if( x == 0 || x-i < i ){ jump(x-i, i+1, M); }
	if( re >= 0 ){ return re; }
	re = jump(x, i+1, M);
	if( re >= 0 ){ return re; }
	if( x==0 || x+i > i ){ re = jump(x+i, i+1, M); }
	if( re >= 0 ){ return re; }
	return re;
}

int main(){
	int re = -1;
	std::cin >> X;
	for( int i = 1; i <= X; i++ ){
		std::cout << "i:" << i << std::endl;
		if( GM(i) < X ){ continue; }
		re = jump(0, 1, i);
		if( re >= 0 ){
			std::cout << re << std::endl;
			break;
		}
	}
	return 0;
}
*/