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: Accepted)

#include <bits/stdc++.h>

#define REP(i, x) REPI(i, 0, x)
#define REPI(i, a, b) for (int i = int(a); i < int(b); ++i)
#define ALL(x) (x).begin(), (x).end()

typedef long long ll;
using namespace std;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll X;
  cin >> X;

  vector<ll> sum(100010, 0);
  map<ll, ll> m;

  for (ll i = 1; i < 1e5; ++i) {
    sum.at(i) = sum.at(i - 1) + i;
    m.insert(make_pair(sum.at(i), i));
  }

  ll c = *lower_bound(sum.begin(), sum.end(), X);
  cout << m.at(c) << endl;

  return 0;
}