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)

#![allow(unused_imports)]
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

use nyan::*;

fn main() {
    let stdin = std::io::stdin();
    let mut sc = Scanner::new(stdin.lock());

    let k: u64 = sc.read();
    let n: usize = sc.read();
    let a: Vec<u64> = sc.read_vec(n);

    let mut m = a[0] + k - a[n - 1];
    for i in 1..n {
        m = max(m, a[i] - a[i - 1]);
    }

    println!("{}", k - m);
}

#[allow(dead_code)]
mod nyan {
    use std::cmp::Ordering;
    use std::fmt::{Debug, Display};
    use std::io;
    use std::iter::{self, FromIterator};
    use std::str::FromStr;

    // https://doc.rust-lang.org/1.39.0/src/core/num/mod.rs.html#4473-4523
    #[inline]
    pub fn is_ascii_whitespace(c: char) -> bool {
        match c {
            '\t' | '\n' | '\x0C' | '\r' | ' ' => true,
            _ => false,
        }
    }

    #[inline]
    pub fn is_ascii_linebreak(c: char) -> bool {
        match c {
            '\n' | '\r' => true,
            _ => false,
        }
    }

    pub struct Scanner<R: io::BufRead> {
        reader: R,
        buffer: String,
        cursor: usize,
    }

    impl<R: io::BufRead> Scanner<R> {
        pub fn new(reader: R) -> Scanner<R> {
            Scanner {
                reader: reader,
                buffer: String::with_capacity(32),
                cursor: 0,
            }
        }

        fn next<F: Fn(char) -> bool>(&mut self, f: F) -> io::Result<&str> {
            loop {
                if let Some(l) = self.buffer[self.cursor..].find(|c| !is_ascii_whitespace(c)) {
                    self.cursor += l;
                    break;
                }

                self.buffer.clear();
                self.cursor = 0;
                match self.reader.read_line(&mut self.buffer) {
                    Err(e) => return Err(e),
                    Ok(0) => return Err(io::Error::from(io::ErrorKind::UnexpectedEof)),
                    _ => (),
                }
            }

            let start = self.cursor;
            self.cursor = self.buffer[self.cursor..]
                .find(f)
                .map_or(self.buffer.len(), |l| start + l);
            Ok(&self.buffer[start..self.cursor])
        }

        fn next_word(&mut self) -> io::Result<&str> {
            self.next(|c| is_ascii_whitespace(c))
        }

        fn next_line(&mut self) -> io::Result<&str> {
            self.next(|c| c == '\n' || c == '\r')
        }

        pub fn read<T>(&mut self) -> T
        where
            T: FromStr,
            <T as FromStr>::Err: Debug,
        {
            self.next_word().unwrap().parse().unwrap()
        }

        pub fn read_vec<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromStr,
            <U as FromStr>::Err: Debug,
        {
            (0..n).map(|_| self.read()).collect()
        }

        pub fn read_vec2d<T, U, V>(&mut self, m: usize, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<V>,
            V: FromStr,
            <V as FromStr>::Err: Debug,
        {
            (0..m).map(|_| self.read_vec(n)).collect()
        }

        pub fn read_line<T: FromIterator<char>>(&mut self) -> T {
            self.next_line().unwrap().chars().collect()
        }

        pub fn read_lines<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<char>,
        {
            (0..n).map(|_| self.read_line()).collect()
        }
    }

    #[test]
    fn test_scanner_next_word() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert_eq!(r.next_word().unwrap(), "foo");
        assert_eq!(r.next_word().unwrap(), "bar");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    #[test]
    fn test_scanner_next_line() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_line().unwrap(), "hello world");
        assert_eq!(r.next_line().unwrap(), "foo");
        assert_eq!(r.next_line().unwrap(), "bar");
        assert!(r.next_line().is_err());
        assert!(r.next_line().is_err());
    }

    #[test]
    fn test_scanner_no_linebreak() {
        let buf = io::Cursor::new(b"hello world");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    pub fn print_vec<T: Display>(v: &[T]) {
        if v.is_empty() {
            return;
        }

        print!("{}", v[0]);
        for i in v.iter().skip(1) {
            print!(" {}", i);
        }
        println!();
    }

    // C++ like binary search functions (upper_bound, lower_bound, equal_range)
    pub trait BinarySearch<T> {
        fn lower_bound(&self, value: &T) -> usize;
        fn upper_bound(&self, value: &T) -> usize;
        fn equal_range(&self, value: &T) -> (usize, usize) {
            (self.lower_bound(value), self.upper_bound(value))
        }
    }

    impl<T: Ord> BinarySearch<T> for [T] {
        // https://en.cppreference.com/w/cpp/algorithm/lower_bound#Possible_implementation
        fn lower_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Less => first = mid + 1,
                    _ => last = mid,
                }
            }
            first
        }

        // https://en.cppreference.com/w/cpp/algorithm/upper_bound#Possible_implementation
        fn upper_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Greater => last = mid,
                    _ => first = mid + 1,
                }
            }
            first
        }
    }

    #[test]
    pub fn test_binary_search() {
        let data = vec![1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6];
        assert_eq!(data.lower_bound(&4), 7);
        assert_eq!(data.upper_bound(&4), 10);
    }

    // https://doc.rust-lang.org/std/cmp/struct.Reverse.html
    #[derive(PartialEq, Eq, Debug)]
    pub struct Rev<T>(pub T);

    impl<T: PartialOrd> PartialOrd for Rev<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }

    impl<T: Ord> Ord for Rev<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    // Extended Euclidean algorithm
    // ax + by = gcd(x, y)
    pub fn extended_gcd(a: u64, b: u64) -> (u64, i64, i64) {
        if b == 0 {
            (a, 1, 0)
        } else {
            let (m, y, x) = extended_gcd(b, a % b);
            (m, x, y - (a / b) as i64 * x)
        }
    }

    pub fn gcd(a: u64, b: u64) -> u64 {
        if b == 0 {
            a
        } else {
            gcd(b, a % b)
        }
    }

    pub fn lcm(a: u64, b: u64) -> u64 {
        a / gcd(a, b) * b
    }

    // x^n (mod p)
    pub fn pow_mod(mut x: u64, mut n: u64, p: u64) -> u64 {
        let mut r = 1;
        while n > 0 {
            if n & 1 > 0 {
                r *= x;
                r %= p;
            }
            x *= x;
            x %= p;
            n >>= 1;
        }
        r
    }

    #[test]
    fn test_pow_mod() {
        assert_eq!(pow_mod(4, 13, 497), 445);
        assert_eq!(pow_mod(2, 90, 13), 12);
        assert_eq!(pow_mod(2, 99999999, 147), 134);
    }

    // a^{p-1} = 1 (mod p) (Fermat's little theorem)
    // a^{p - 2} * a = 1 → a^{-1} = a^{p-2}
    pub fn inv_mod(n: u64, p: u64) -> u64 {
        pow_mod(n, p - 2, p)
    }

    // s * (s + 1) * .. * t (mod p)
    pub fn prod_mod(s: u64, t: u64, p: u64) -> u64 {
        (s..t + 1).fold(1, |acc, x| acc * x % p)
    }

    // nCk (mod p)
    pub fn comb_mod(n: u64, k: u64, p: u64) -> u64 {
        // nCk = n! / (k! * (n - k)!)
        //     = ((n-k+1) * (n-k+2) * ... * n) * inv(k!)
        prod_mod(n - k + 1, n, p) * inv_mod(prod_mod(1, k, p), p) % p
    }

    // comb_mod_multi(n_max, p)(n, k) = nCk (mod p)
    pub fn comb_mod_multi(n_max: u64, p: u64) -> Box<Fn(u64, u64) -> u64> {
        // fact[n] = n!, fact_inv[n] = (n!)^(-1) (mod p)
        let fact = iter::once(1)
            .chain(1..n_max + 1)
            .scan(1, |state, x| {
                *state = (*state * x) % p;
                Some(*state)
            })
            .collect::<Vec<_>>();
        let fact_inv = fact.iter().map(|&x| inv_mod(x, p)).collect::<Vec<_>>();

        Box::new(move |n, k| {
            let a = fact[n as usize];
            let b = fact_inv[k as usize];
            let c = fact_inv[(n - k) as usize];
            (((a * b) % p) * c) % p
        })
    }

    #[inline]
    pub fn minmax<T: Ord>(a: T, b: T) -> (T, T) {
        if a < b {
            (a, b)
        } else {
            (b, a)
        }
    }

    #[test]
    fn test_minmax() {
        assert_eq!(minmax(1, 3), (1, 3));
        assert_eq!(minmax(3, 1), (1, 3));
    }

    #[inline]
    pub fn digits(x: u64, base: u64) -> u32 {
        (1..)
            .find(|&i| base.pow(i - 1) <= x && x < base.pow(i))
            .unwrap_or(0)
    }

    #[test]
    fn test_digits() {
        assert_eq!(digits(1234, 10), 4);
        assert_eq!(digits(1234567890, 10), 10);
        assert_eq!(digits(0xdeadbeef, 16), 8);
        assert_eq!(digits(0o123456, 8), 6);
        assert_eq!(digits(0b10101, 2), 5);
    }

    pub struct UnionFind {
        n: usize,
        root: Vec<usize>,
        rank: Vec<usize>,
        size: Vec<usize>,
    }

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            UnionFind {
                n: n,
                root: (0..n).collect(),
                rank: vec![0; n],
                size: vec![1; n],
            }
        }

        pub fn root(&mut self, x: usize) -> usize {
            let r = self.root[x];
            if r == x {
                r
            } else {
                self.root[x] = self.root(r);
                self.root[x]
            }
        }

        pub fn merge(&mut self, x: usize, y: usize) {
            let rx = self.root(x);
            let ry = self.root(y);
            if rx == ry {
                return;
            }

            if self.rank[rx] < self.rank[ry] {
                self.root[rx] = ry;
                self.size[ry] += self.size[rx];
            } else {
                self.root[ry] = rx;
                self.size[rx] += self.size[ry];
                if self.rank[rx] == self.rank[ry] {
                    self.rank[rx] += 1;
                }
            }
        }

        pub fn size(&mut self, x: usize) -> usize {
            let rx = self.root(x);
            self.size[rx]
        }
    }
}