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: Wrong Answer)

#include<bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define ll long long 
#define pll pair<ll,ll>
#define vll vector<pll>
#define vl vector<ll>
#define f first
#define s second
#define N 50000
#define pb push_back
#define mp make_pair
#define MAP map<ll,ll>
#define INF 1000000000
#define mod 1000000007
#define foo(i,a,b) for(ll i=(a);i<=(b);i++)
#define rep(i,a,b) for(ll i=(a);i>=(b);i--)
#define sl set<ll> 
#define sll set<pll>
#define ub upper_bound
#define lb lower_bound
using namespace std;

//<<-----Declare Variable Here------->>//
ll k,n,a[200000],cnt1=0;sl A,b; 
 
//<<-----Implement Functions Here---->>//
 
 
//<<-----Start of Main--------------->>//
void MAIN(){
	cin>>k>>n;
	foo(i,0,n-1) cin>>a[i];
	sort(a,a+n);
	ll ans=a[n-1]-a[0];
	ll j=n-1,sum=a[0],start=-1;
	foo(i,0,n-1){
		if(a[i]>k/2) a[i]-=k;  
	}

	// ll x=start>-1?start:n;
	// foo(i,x,n-1) a[i]-=k;
	sort(a,a+n);
	cout<<min(ans,a[n-1]-a[0])<<"\n";

}

int main(){
	fastio;
 	ll t=1;
	//cin>>t;
	while(t--){
		MAIN();
	}
 
    // #ifndef ONLINE_JUDGE
    // cout<<"\nTime Elapsed: " << 1.0*clock() / CLOCKS_PER_SEC << " sec\n";
    // #endif
}