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++14 (GCC 5.4.1) (judge verdict: Accepted)

//Konrad Paluszek,University of Warsaw(former XIV LO Staszic)
#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#define TIME (chrono::steady_clock::now().time_since_epoch().count())
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define xfm(a,b)a##b
#define xwb(a,b)xfm(a,b)
#define _ xwb(nvj,__LINE__)
#define __ xwb(kjy,__LINE__)
#define ___ xwb(cjm,__LINE__)
#define REP(i,n)for(urs(n)i=0;i<(n);++i)
#define UNTIL(t)while(clock()<(t)*CLOCKS_PER_SEC)
#define PER(r...)for(bool _=1;_||next_permutation(r);_=false)
#define ALL(r)(r).begin(),(r).end()
#define RALL(r)(r).rbegin(),(r).rend()
#define FS(r)r.first,r.second
#define SF(r)r.second,r.first
#define M0(r) memset(r, 0, sizeof(r))
#define sim template<class c
#define ros return o
#define rans return ans
#define forbits(i,m)if(m)for(urs(m)i=ctz(m),i##nvj=m;i##nvj;i##nvj^=((urs(m))1<<i),i=ctz(i##nvj))
#define fordbits(i,m)if(m)for(urs(m)i=8*sizeof(m)-clz(m)-1,i##nxd=m;i##nxd;i##nxd^=((urs(m))1<<i),i=8*sizeof(m)-clz(i##nxd)-1)
#define ksets(t, m, k, n) for (t m = (((t)1 << (k)) - 1); m < ((t)1 << (n)); m = nux(m))
#define urs(r...)typename decay<decltype(r)>::type
#define hur(f,g,r)sim>int f(c a){if(sizeof(c)==16)return r;if(sizeof(c)==8)return g##ll(a);return g(a);}
#define pwq(t,i) int clz(t x){return clz<int>(x)-i;}
using namespace __gnu_pbds;using namespace std;using ll=long long;using ld=long double;using ull=unsigned long long;using vi=vector<int>;using pii=pair<int,int>;using pll=pair<ll,ll>;using vpii=vector<pii>;using spii=set<pii>;using mii=map<int,int>;using unt=unsigned int;sim>using min_queue=priority_queue<c,vector<c>,greater<c>>;sim,class b,class cmp=less<c> >using ordered_map=tree<c,b,cmp,rb_tree_tag,tree_order_statistics_node_update>;sim, class cmp=less<c>>using ordered_set = ordered_map<c,null_type,cmp>;hur(popc,__builtin_popcount,popc<ull>(a)+popc<ull>(a>>64))hur(ctz,__builtin_ctz,(ull)a?ctz<ull>(a):64+ctz<ull>(a>>64))hur(clz,__builtin_clz,a>>64?clz<ull>(a>>64):64+clz<ull>(a))pwq(short,16)pwq(uint16_t,16)pwq(char,24)pwq(int8_t,24)pwq(uint8_t,24)sim,class N>bool mini(c&o,const N&h){if(o>h)ros=h,1;return 0;}sim,class N>bool maxi(c&o,const N&h){if(o<h)ros=h,1;return 0;}sim,class n>using gyv=c;
#if defined(LOCAL) // || defined(LOCAL2)
#include </home/kjp/headers/debuglib.hpp>
#else
#define loc(...)
#define onl(r...)r
#define debug(...)
#define print_stack(...)
#define mark_stack(...)
#define set_pre(...)
#define reg_it(...)
#endif
#define next nexT
#define prev preV
#define tree trEE
#define left lefT
#define right righT
#define div diV
#define y1 y_1
ull mix(ull o){o+=0x9e3779b97f4a7c15;o=(o^(o>>30))*0xbf58476d1ce4e5b9;o=(o^(o>>27))*0x94d049bb133111eb;ros^(o>>31);}ull SALT=0x7a14a4b0881ebf9,tqu=0x7a14a4b0881ebf9;ull my_rand(){return tqu=mix(tqu);}void my_srand(ull x){SALT=tqu=x;}const int inf = 1023400000;const ll llinf=1234567890000000000ll;ll fix(ll o, ll m){o%=m;if(o<0)o+=m;ros;}
#define rand my_rand
#define srand my_srand
#define random_shuffle(r...)random_shuffle(r,[](int _){return my_rand()%_;})
sim>inline c nux(c m){if(!m)return numeric_limits<c>::max();c A=m&-m;c B=~((A-1)^m);c C=B&-B;c D=(C>>(1+ctz(A)))-1;return C|(m&~(C-1))|D;}__attribute__((no_sanitize_undefined))ll mul(ll a,ll b,ll m){ll q=a*(ld)b/m;ll o=a*b-q*m;o%=m;if(o<0)o+=m;ros;}sim>void unq(c&x){x.resize(unique(ALL(x))-x.begin());}
#if ((ULONG_MAX) != (UINT_MAX))
namespace std {template <> struct is_signed<__int128> : public true_type {};}
#endif
sim, class d> typename common_type<c,d>::type floor_div(c a, d b) {static_assert(is_signed<c>::value==is_signed<d>::value,"using floor_div with different signedness");if (b < 0) b = -b, a = -a;return a / b - (a % b < 0);}
sim, class d> typename common_type<c,d>::type ceil_div(c a, d b) {static_assert(is_signed<c>::value==is_signed<d>::value,"using ceil_div with different signedness");if (b < 0) b = -b, a = -a;return a / b + (a % b > 0);}
sim> struct REV {c &x;using it=typename c::reverse_iterator;it begin(){return x.rbegin();}it end(){return x.rend();}};
sim> struct CREV {const c&x;using it=typename c::const_reverse_iterator;it begin(){return x.rbegin();}it end(){return x.rend();}};
sim> REV<c> reversed(c&x) {return REV<c>{x};}sim> CREV<c> reversed(const c&x) {return CREV<c>{x};}
#define done(r...) exit(0 * printf(r))
#if defined(LOCAL) || defined(LOCAL2)
void __tmi() {cerr << setprecision(6) << fixed << "total time: " << clock() / (ld)CLOCKS_PER_SEC << "s" << endl;}int _ = (atexit(__tmi), 0);
#endif
int main() {
	int k, n;
	scanf("%d%d", &k, &n);
	vi v(n);
	REP(i, n) scanf("%d", &v[i]);
	int lon = 0;
	REP(i, n - 1) maxi(lon, v[i + 1] - v[i]);
	maxi(lon, v[0] + k - v.back());
	printf("%d\n", k - lon);
}