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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++)
typedef long long ll;
using namespace std;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	ll x,sum=0,a,b,c,s;
	cin>>x;
	for(int i=1;i<1000000001;i++){
		sum+=i;
		if(sum==x){
			cout<<i<<endl;
			return 0;
		}
		if(sum>x){
			s=sum;
			sum-=i;
			sum-=i-1;
			a=x-sum;
			b=i+(x-(s-i))*2-1;
			c=i+1+(s-x)*2-1;
			if(b>=0 && c>=0){
			  cout<<min({a,b,c})<<endl;
			}else if(b>=0 && c<0){
				cout<<min({a,b})<<endl;
			}else if(b<0 && c>=0){
				cout<<min({a,c})<<endl;
			}else if(b<0 && c<0){
				cout<<a<<endl;
			}
			return 0;
		}
	}
	return 0;
}