Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

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

use std::io;

fn main() {
    // 一行目を取得、分割
    let mut one_line_buffer = String::new();

    io::stdin().read_line(&mut one_line_buffer).unwrap();
    let one_line_vec: Vec<i64> = one_line_buffer
        .trim()
        .split_whitespace()
        .map(|c| c.parse().unwrap())
        .collect();

    let lake_circumference: i64 = one_line_vec[0];
    let house_num: usize = one_line_vec[1] as usize;

    // 二行目を取得、分割
    let mut two_line_buffer = String::new();
    io::stdin().read_line(&mut two_line_buffer).unwrap();

    let house_distances_from_north: Vec<i64> = two_line_buffer
        .trim()
        .split_whitespace()
        .map(|c| c.parse().unwrap())
        .collect();

    // for i in &house_distances_from_north {
    //     println!("{}", i);
    // }

    // 隣の家間の距離を計算
    let mut house_distances_from_previous: Vec<i64> = vec![];

    house_distances_from_previous.push(
        house_distances_from_north[0]
            + (lake_circumference - house_distances_from_north[house_num - 1]),
    );

    // 家間の最大距離とそのindex
    let mut max_distance: i64 = house_distances_from_previous[0];

    // println!("0: {}", house_distances_from_previous[0]);

    for i in 1..house_num {
        house_distances_from_previous
            .push(house_distances_from_north[i] - house_distances_from_north[i - 1]);

        if house_distances_from_previous[i] > max_distance {
            max_distance = house_distances_from_previous[i];
        }

        // println!("{}: {}", i, house_distances_from_previous[i]);
    }

    let mut distance_sum: i64 = 0;

    for i in house_distances_from_previous {
        distance_sum += i;
    }

    println!("{}", distance_sum - max_distance);
}