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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"reflect"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	sc.Split(bufio.ScanWords)
	defer out.Flush() // !!!!coution!!!! you must use Fprint(out, ) not Print()
	/* --- code --- */
	K, N := nextInt(), nextInt()
	A := make([]int, N)
	for i := 0; i < N; i++ {
		A[i] = nextInt()
	}
	maxL := K - (A[N-1] - A[0])
	for i := 1; i < N; i++ {
		maxL = max(maxL, A[i]-A[i-1])
	}
	fmt.Println(K - maxL)
}
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}
func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// -*-*-*-*-*-*-*-*-
// * I/O utilities *
// -*-*-*-*-*-*-*-*-

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

func nextInt64() int64 {
	a, _ := strconv.ParseInt(next(), 10, 64)
	return a
}

func nextFloat64() float64 {
	a, _ := strconv.ParseFloat(next(), 64)
	return a
}

func nextInts(n int) []int {
	ret := make([]int, n)
	for i := 0; i < n; i++ {
		ret[i] = nextInt()
	}
	return ret
}
func nextFloats(n int) []float64 {
	ret := make([]float64, n)
	for i := 0; i < n; i++ {
		ret[i] = nextFloat64()
	}
	return ret
}
func nextStrings(n int) []string {
	ret := make([]string, n)
	for i := 0; i < n; i++ {
		ret[i] = next()
	}
	return ret
}

func split(s string) []string {
	ret := make([]string, len([]rune(s)))
	for i, v := range []rune(s) {
		ret[i] = string(v)
	}
	return ret
}

func PrintOut(src interface{}, joinner string) {
	switch reflect.TypeOf(src).Kind() {
	case reflect.Slice:
		s := reflect.ValueOf(src)
		for idx := 0; idx < s.Len(); idx++ {
			fmt.Fprintf(out, "%v", s.Index(idx))
			if idx < s.Len()-1 {
				fmt.Fprintf(out, "%s", joinner)
			} else {
				fmt.Fprintln(out)
			}
		}
	default:
		fmt.Fprintln(out, "fuck")
	}
}

// -*-*-*-*-*-*-*-*-
// * tool snippets *
// -*-*-*-*-*-*-*-*-
func duplicate2Int(base [][]int) (ret [][]int) {
	ret = make([][]int, len(base))
	for i, v := range base {
		ret[i] = append([]int{}, v...)
	}
	return
}

// -*-*-*-*-*-*-*-*-*-*-*-*-*-
// * Algorithms Utility Zone *
// -*-*-*-*-*-*-*-*-*-*-*-*-*-

// -*-*-*-*-*-*-*-
// * 1. nibutan  *
// -*-*-*-*-*-*-*-
func lower_bound(arr []int, target int) int {
	l, r := 0, len(arr)
	for l < r {
		mid := (l + r) / 2
		if arr[mid] < target {
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}

func upper_bound(arr []int, target int) int {
	l, r := 0, len(arr)
	for l < r {
		mid := (l + r) / 2
		if target < arr[mid] {
			r = mid
		} else {
			l = mid + 1
		}
	}
	return l
}

// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
// * math flavor typical theories *
// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
func gcd(a, b int) int {
	if a > b {
		return gcd(b, a)
	}
	for a != 0 {
		a, b = b%a, a
	}
	return b
}

func pow(a, b int) (ret int) {
	ret = a
	// 10^2 = 100ってことは10に10を1回掛けることだね
	// なので初期値を含めると上限b-1未満
	for i := 0; i < b-1; i++ {
		ret *= a
	}
	return
}

func powMod(n, m, mod int) (ret int) {
	ret = 1
	for m > 0 {
		if m&1 == 1 {
			ret *= n
			ret %= mod
		}
		n *= n
		n %= mod
		m >>= 1
	}
	return ret
}