/*
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	でかいですね。
	更にかわいいときた。
	うん。好き。
*/

/*  include  */
#include <assert.h>
#include <ctype.h>
#include <errno.h>
#include <locale.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <setjmp.h>
#include <string.h>
#include <signal.h>
#include <stdarg.h>
#include <stdbool.h>

/*  typedef  */
typedef long long ll;
typedef char string[100];
typedef int array[100];
/*  define  */

/*  define funcs  */
#define sort_d(array,end){int size=end-array;qsort(array,size,sizeof(int),intcmp);}
#define sort_c(array,end){int size=end-array;qsort(array,size,sizeof(char),charcmp);}
#define rand_range(min,max) (min)+(rand())%((max)-(min)+(1))
#define rep(i,j) for(int i=0;i<j;i++)
#define loop(i,j,z) for(int i=j;i<z;i++)
#define swap(a,b) ((a!=b)&&(a+=b,b=a-b,a-= b))
#define getarray_d(array,size){array=(int *)malloc(sizeof(int)*size);}
#define getarray_c(array,size){array=(char *)malloc(sizeof(char)*size);}
#define fill(array,end,val){int size=end-array;rep(i,size)array[i]=val;}
#define min(a,b) (a>b)?b:a
/*  otter  (Otter)  ｶﾜｳｿｯ！ */
#define intptr int *
#define random srand((unsigned)time(NULL))
#define ON 1
#define OFF 0
#define TREE_SIZE 1000

/*  prototype Declaration */
int intcmp(const void* a, const void* b);
int charcmp(const void* a, const void* b);
bool is_sorted(const int* start, const int* end);
int count(const int* start, const int* end, int target);
void shuffle(int* start, int* end);
void tree_init(void);
int tree_root(int x);
void unite(int x, int y);
bool same(int x, int y);

/*  scan  */
#define sd(a) scanf("%d",&a)
#define sc(a) scanf("%c",&a), getchar()
#define sf(a) scanf("%f",&a)
#define ss(a) scanf("%s",a)
#define sld(a) scanf("%lld",&a)
/*  print  */
#define odn(a) printf("%d\n",a)
#define oldn(a) printf("%lld\n",a)
#define ocn(a) printf("%c\n",a)
#define ofn(a) printf("%f\n",a)
#define osn(a) printf("%s\n",a)
#define od(a) printf("%d ",a)
#define old(a) printf("%lld\n",a)
#define oc(a) printf("%c ",a)
#define of(a) printf("%f ",a)
#define os(a) printf("%s ",a)

/*  struct  */
typedef struct {
	int first;
	int second;
}pair;
/*  local val  */
int tree[TREE_SIZE];
int cnts=0;
/*  funcs （local）*/

/*  main program  */
int main(void){
	int K,N;
	int A[200005];
	sd(K),sd(N);
	rep(i,N) sd(A[i]);
	int m_len=INT_MAX;
	rep(i,N){
		if(i!=N-1)
			m_len=min(m_len,K-(A[i+1]-A[i]));
		else
			m_len=min(m_len,A[N-1]-A[0]);
	}
	od(m_len);
}

/*  funcs  (global)*/
void sort_first(pair* b, pair* e)
{
	int* dec;
	int s2 = e - b;
	int size = e - b;
	getarray_d(dec, size);
	rep(i, size) dec[i] = b[i].first;
	sort_d(dec, dec + s2);
	rep(i, size) b[i].first = dec[i];
}
void sort_second(pair* b, pair* e)
{
	int* dec;
	int s2 = e - b;
	int size = e - b;
	getarray_d(dec, size);
	rep(i, size) dec[i] = b[i].second;
	sort_d(dec, dec + s2);
	rep(i, size) b[i].second = dec[i];
}


int intcmp(const void* a, const void* b)
{
	return *(int*)a - *(int*)b;
}

int charcmp(const void* a, const void* b)
{
	return *(char*)a - *(char*)b;
}

bool is_sorted(const int* start, const int* end)
{
	while (start != end) {
		if (*start > * (start + 1)) return false;
		start++;
	}
	return true;
}

int count(const int* start, const int* end, int target)
{
	int cnt = 0;
	int* array;
	int* p;

	array = (int*)malloc((end - start) * sizeof(int));

	if (array == NULL) {
		printf("Err0r");
		exit(-1);
	}

	memcpy(array, start, sizeof(int) * (end - start));
	sort_d(array, array + (end - start));
	p = (int*)bsearch(&target, array, end - start, sizeof(int), intcmp);

	if (p == NULL) {
		free(array);
		return 0;
	}
	while (*p == target)
		p++;
	p--;
	while (*p == target) {
		cnt++;
		p--;
	}

	free(array);

	return cnt;
}

void shuffle(int* start, int* end)
{
	random;

	int a, b;
	int size = end - start;

	rep(i, 500) {
		a = rand_range(0, size - 1);
		b = rand_range(0, size - 1);
		swap(start[a], start[b]);
	}
}
/*  tree  */

void tree_init(void)
{
	for (int i = 0; i < TREE_SIZE; i++) tree[i] = i;
}

int tree_root(int x)
{
	if (tree[x] == x) return x;
	return tree[x] = tree_root(tree[x]);
}

void unite(int x, int y)
{
	int rx = tree_root(x);
	int ry = tree_root(y);
	if (rx == ry) return;
	tree[rx] = ry;
}

bool same(int x, int y)
{
	int rx = tree_root(x);
	int ry = tree_root(y);
	return rx == ry;
}

ll pow_mod(ll n, ll k, ll m)
{
	if (k == 0) return 1;
	else if (k % 2) return pow_mod(n, k - 1, m) * n % m;
	else {
		int t = pow_mod(n, k / 2, m);
		return t * t % m;
	}
}


Measured memory_bytes: 896