Problem:
Score : 200 points

Problem Statement

There are N + 1 squares arranged in a row, numbered 0, 1, ..., N from left to right.

Initially, you are in Square X.
You can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.
However, for each i = 1, 2, ..., M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.
It is guaranteed that there is no toll gate in Square 0, Square X and Square N.

Find the minimum cost incurred before reaching the goal.

Constraints

1 \leq N \leq 100

1 \leq M \leq 100

1 \leq X \leq N - 1

1 \leq A_1 < A_2 < ... < A_M \leq N

A_i \neq X

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M X
A_1 A_2 ... A_M

Output

Print the minimum cost incurred before reaching the goal.

Sample Input 1

5 3 3
1 2 4

Sample Output 1

1

The optimal solution is as follows:

First, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.

Then, travel from Square 4 to Square 5. This time, no cost is incurred.

Now, we are in Square 5 and we have reached the goal.

In this case, the total cost incurred is 1.

Sample Input 2

7 3 2
4 5 6

Sample Output 2

0

We may be able to reach the goal at no cost.

Sample Input 3

10 7 5
1 2 3 4 6 8 9

Sample Output 3

3

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;

fn lower_bound(v: &Vec<i32>, x: i32) -> i32 {
    let mut l: i32 = 0;
    let mut r: i32 = v.len() as i32;

    loop {
        if l==r {
            break;
        }
        let c: i32 = (l + r)/2;
        match v[c as usize].cmp(&x) {
            std::cmp::Ordering::Less => {
                l = c + 1;
            }
            std::cmp::Ordering::Equal | std::cmp::Ordering::Greater => {
                r = c;
            }
        }
    }
    l
}

fn main() {
    let mut buf = String::new();
    let _ = std::io::stdin().read_to_string(&mut buf);
    let mut it = buf.split_whitespace();
    let n: i32 = it.next().unwrap().parse().unwrap();
    let m: i32 = it.next().unwrap().parse().unwrap();
    let x: i32 = it.next().unwrap().parse().unwrap();
    let a: Vec<i32> = (0..m).map(|_| {
        it.next().unwrap().parse().unwrap()
    }).collect();

    let x_idx = lower_bound(&a, x);
    let ans = std::cmp::min(x_idx, m-x_idx);
    println!("{}", &ans);
}