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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>


int compare_int(const void *a, const void *b)
{
    return *(int*)a - *(int*)b;
//    return *(long long*)a - *(long long*)b;
}
//  qsort(A, b, sizeof(int), compare_int);

//long long  factorial(long long n) {
//    if (n > 0) {
//        return n * factorial(n - 1);
//    } else {
//        return 1;
//    }
//}
long long  factorial(long long n, long long depth) {
    if (n > 1) {
        depth++;
        return factorial(n / 2, depth);
    } else {
        return depth;
    }
}

int min(int a, int b) {
    if (a > b)
        return b;
    else
        return a;
}

int distance(int a, int b) {
  return abs(a-b)*abs(a-b);
}



//int ()
/*
int triangle(int a, int b, int c){
  if(a<b+c){
    if(b<c+a){
      if(c<a+b){
        printf("1\n");
        return 1;
      }
    }
  }
  printf("1\n");
  return 0;
}
*/

int main()
{
  int  a, b, c, d, e, X, Y ,r;
//  unsigned long long  a, b, c, d, e, X, Y;
  //  double  c;
// long long  A[200003]={};
  int  A[200003]={};
  int  B[100003]={};
//  int  C[100003][100001]={};
  int  C[100003]={};

  int  flg=0;

//  char s[101][101]={};
  char s[100001]={};
  char t[100001]={};
//  int N, M;
//  int A[1000000001]={};
//  long long  C[101]={};
  int i,j,k;
  long long p=0,q=0;
//  int flag=0;
//  int tmp=0;
//  char tmp[101]={};
//  long long min=10000000000;
//  long long min=100000001;
  int min =100000001;
  int len=0;
  int l=0;
//  int r=1000001;
  int cnt=0;
  int num=0;
  int num1=0;
  int num2=0;
  long long  ans=0;
  int ans_ac=0;
  int ans_wa=0;
  int max=0;
  long long sum=0;
  int addr=0;
  int ptn=0;
  int  tmp=0;
  double per=0; 
//  bool on_off[100]={};
  
//  char alp[26]={'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z'};

  //  a=0;
  scanf("%d %d", &a, &b);
  
  for(i=0;i<b;i++){
    scanf("%d",&A[i]);
  }
//  qsort(A, b, sizeof(int), compare_int);
  for(i=1;i<b;i++){
//    printf("%d\n",A[i]-A[i-1]);
    if(max<(A[i]-A[i-1])) max=A[i]-A[i-1];
  }
//    printf("%d\n",A[b-1]-A[0]);

  if(max<((a-A[b-1])+A[0])) max=(a-A[b-1])+A[0];
    printf("%d\n",a-max);
  
return 0;
}