#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<vector>
#include<queue>
#include<algorithm>
#include<string>
#include<sstream>
#include<cctype>
#include<cmath>
#include<iomanip>
#include<map>
#include<stack>
#include<set>
#include<functional>
#define in(x) x=read()
#define qr read()
#define int ll
#define mp make_pair
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
namespace fastIO
{
    #define BUF_SIZE 100000
    bool IOerror=0;
    inline char nc()
	{
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if (p1==pend){
            p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if (pend==p1){IOerror=1;return -1;}
        }
        return *p1++;
    }
    inline bool blank(char ch){return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';}
    inline ll read()
	{
        bool sign=0; char ch=nc();ll x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return 0;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (sign)x=-x;
        return x;
    }
    #undef BUF_SIZE
};
using namespace fastIO;
int n,m,x[1000010],y[1000010];
bool check(int l)
{
	int mn=1,mx=2*n;;
	for(int i=1;i<=m;i++)
	{
		int lp,rp;
		if(y[i]-x[i]<=l)
		{
			if(x[i]+n-y[i]<=l)lp=1,rp=2*n;
			else lp=y[i],rp=x[i]+n;
		}
		else if(x[i]+n-y[i]<=l)lp=x[i],rp=y[i];
		else return 0;
		mn=max(mn,lp),mx=min(mx,rp);
	}
	return mn<mx;
}
signed main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	while(n=qr,m=qr)
	{
		for(int i=1;i<=m;i++)
		{
			in(x[i]),in(y[i]);
			if(x[i]>y[i])swap(x[i],y[i]);
		}
		int l=0,r=n,ans;
		while(l<=r)
		{
			int mid=(l+r)/2;
			if(check(mid))ans=mid,r=mid-1;
			else l=mid+1;
		}
		cout<<ans<<'\n';
		n=0,m=0;
	}
	return 0;
}