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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::stdin;

fn main(){
    let x = getvec()[0];
    println!("{}", solve(x, 0, 100000))
}

fn solve(x: i64, a: i64, b: i64) -> i64{
    if a+1==b {
        b
    } else if sum_((a+b)/2)<x {
        solve(x, (a+b)/2, b)
    } else{
        solve(x, a, (a+b)/2)
    }
}

fn sum_(x: i64) -> i64{
    x * (x+1) / 2
}

#[allow(dead_code)]
fn getline() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn getvec() -> Vec<i64>{
    let line = getline();
    line.split_whitespace().map(|x| x.parse().unwrap()).collect()
}

#[allow(dead_code)]
fn getpair() -> (i64, i64){
    let nm = getvec();
    (nm[0], nm[1])
}