#include<bits/stdc++.h>
using namespace std;
#define FS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define ll long long int
#define MAX_INT 100000
#define ld long double
#define pb push_back
#define mp make_pair
#define pu push
#define vsz(v) cout<<v.size()<<endl; 
#define printv(v) for(ll i=0;i<v.size();i++)cout<<v[i]<<" "; cout<<endl;
#define printa(a,n) for(ll i=0;i<n;i++)cout<<a[i]<<" ";cout<<endl;
#define printrv(v) for(ll i=v.size()-1;i>=0;i--)cout<<v[i]<<" "; cout<<endl;
#define printvpair(v) for(ll i=0;i<v.size();i++)cout<<v[i].first<<" "<<v[i].second<<endl;
#define sz size()
#define ff first
#define ss second
#define vll vector<ll>
#define vbool vector<bool>
#define vpll vector<pair<ll,ll>>
#define vvpll vector<vector<pair<ll,ll>>>
#define qll queue<ll>
#define dqll deque<ll>
#define pll pair<ll,ll>
#define vllv vector<vector<ll>> 
#define vstr vector<string>
#define setpri(x) cout<<setprecision(x);
#define all(v) v.begin(),v.end()
#define allr(v) v.rbegin(),v.rend()
#define scana(a,n) for(ll i=0;i<n;i++)cin>>a[i];
#define inf 1000000000000
#define yes cout<<"YES"<<endl
#define no cout<<"NO"<<endl
#define yesr {cout<<"YES"<<endl;return;}
#define nor {cout<<"NO"<<endl;return;}
ll MOD=1e9+7;
ll ceil1(ll n,ll x){if(n%x==0)return n/x; else return (n/x)+1;}
ll gcd(ll a,ll b){return __gcd(a,b);}
ll lcm(ll a,ll b){return (max(a,b)/gcd(a,b))*min(a,b);}
ll pow1(ll n,ll k,ll mm){
    if(k==0)return 1;
    if(k%2==0)return (pow1((n%mm)*(n%mm),k/2,mm))%mm;
    return ((n%mm)*(pow1((n%mm)*(n%mm),k/2,mm)%mm))%mm;
}
ll pow2(ll n,ll k){ll ans=1;
	while(k>0){
        if(k%2==1)ans=ans*n;n=n*n;k/=2;
    }return ans;
}
ll modinv(ll A,ll M){return pow1(A,M-2,M);}
ll fact(ll n){ll s=1; for(ll i=1;i<=n;i++)s*=i; return s;}
ll factmod(ll n,ll mod){ll s=1; for(ll i=1;i<=n;i++){s*=i;s%=mod;} return s;}
vll fact1tonmod(ll n,ll mod){vll  ans(n+1);ans[0]=ans[1]=1;
	for(ll i=2;i<=n;i++)ans[i]=(ans[i-1]*i)%mod;
	return ans;
}
ll ncrmod(ll n,ll r,ll mod){
	ll ans=((((factmod(n,mod)%mod)*(modinv(factmod(r,mod),mod)%mod))%mod)*(modinv(factmod(n-r,mod),mod)))%mod;
	return ans;
}
ll ncr(ll n,ll r){if(n==1 || r==0)return 1;if(r>n/2)r=n-r;
	ll ans=1;for(ll i=1;i<=r;i++){ans=((ans * n )/i);n--;}return ans;
}
ll ncrsum(ll n,ll r, ll mod){
	if(n==1 || r==0)return 1;
	ll ans=1,sum=1;for(ll i=1;i<=r;i++){ans=(((ans * n )/i)%mod);n--;sum+=ans;sum%=mod;}return sum;
}
bool isprime(ll n){if(n==1 || (n!=2 && n%2==0))return false; if(n==2)return true; 
		for(ll i=3;i<=sqrt(n);i+=2)if(n%i==0)return false; return true; }
vll createprime(ll n){
	vector<bool> prime(n+1,true);vll ans;;prime[0]=prime[1]=false;
	for(ll i=2;i*i<=n;i++)if(prime[i])for(ll j=i*i;j<=n;j+=i)prime[j]=false;
	for(ll i=2;i<=n;i++)if(prime[i])ans.pb(i);
	return ans;
}
vbool createprimebool(ll n){
	vector<bool> prime(n+1,true);prime[0]=prime[1]=false;
	for(ll i=2;i*i<=n;i++)if(prime[i])for(ll j=i*i;j<=n;j+=i)prime[j]=false;
	return prime;
}
vll factor(ll n){
	vll ans;
	if(n>0)ans.pb(1);if(n==2)ans.pb(2);
	for(ll i=2;i*i<=n;i++){if(n%i==0){ans.pb(i);if(n/i!=i)ans.pb(n/i);}}if(n>2)ans.pb(n);
	return ans;
}
ll numoffactor(ll n){ return factor(n).sz;}
bool func(pair<ll,ll> &a,pair<ll,ll> &b ){
	if(a.ff != b.ff)return a.ff < b.ff;
	return a.ss > b.ss;
}
void update(vll &tree,vll &lazy,ll node,ll l,ll r,ll start,ll end,ll k){
 
	if(lazy[node]){
 
		tree[node]+=(r-l+1)&lazy[node];
		if(l!=r){
			lazy[2*node]+=lazy[node];
			lazy[2*node+1]+=lazy[node];
		}
		lazy[node]=0;
	}
	if(l>end or r<start)return;
 
	if(l>=start && r<=end){
		tree[node]+=(r-l+1)*k;
		if(l!=r){
			lazy[2*node]+=k;
			lazy[2*node+1]+=k;
		}
		return;
	}
	ll mid=(l+r)/2;
	update(tree,lazy,2*node,l,mid,start,end,k);
	update(tree,lazy,2*node+1,mid+1,r,start,end,k);
	tree[node]=tree[2*node]+tree[2*node+1];
}
ll query(vll &tree,vll &lazy,ll node,ll l,ll r,ll start,ll end){
	if(lazy[node]){
		tree[node]+=(r-l+1)*lazy[node];
		if(l!=r){
			lazy[2*node]+=lazy[node];
			lazy[2*node+1]+=lazy[node];
		}
		lazy[node]=0;
	}
	if(l>end or r<start)return 0;
	if(l>=start && r<=end)return tree[node];
	ll mid=(l+r)/2;
	return query(tree,lazy,2*node,l,mid,start,end)+query(tree,lazy,2*node+1,mid+1,r,start,end);
}
void solve(){
    ll i,j,k,n,l,m,x,y,z,d,r;
	cin>>k>>n;
  vll a(n);
  for(i=0;i<n;i++){
   cin>>a[i]; 
  }
  ll ans=a[0]+k-a[n-1];
  for(i=1;i<n;i++){
   ans=max(ans,a[i]-a[i-1]); 
  }
  cout<<k-ans<<endl;
}
int main(){
	FS;
	ll i,j,k,n,m,x,y,z,q;
	q=1;
	 //cin>>q;
	while(q--){
		solve();
	}
	return 0;
}


Measured memory_bytes: 1792