Problem:
Score : 1000 points

Problem Statement

You are given a string S consisting of digits between 1 and 9, inclusive.
You will insert at most K commas (,) into this string to separate it into multiple numbers.

Your task is to minimize the maximum number among those produced by inserting commas. Find minimum possible such value.

Constraints

0 ≦ K < |S| ≦ 100,000

S consists of digits between 1 and 9, inclusive.

Partial Scores

In the test set worth 100 points, |S| ≦ 2.

In the test set worth another 100 points, |S| ≦ 16.

In the test set worth another 200 points, |S| ≦ 100.

In the test set worth another 200 points, |S| ≦ 2,000.

Input

The input is given from Standard Input in the following format:

K
S

Output

Print the minimum possible value.

Sample Input 1

2
15267315

Sample Output 1

315

When the string is separated into 152, 67 and 315, the maximum among these is 315, which is the minimum possible value.

Sample Input 2

0
12456174517653111

Sample Output 2

12456174517653111

12456174517653111 itself is the answer.

Sample Input 3

8
127356176351764127645176543176531763517635176531278461856198765816581726586715987216581

Sample Output 3

5317635176

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static Sa sa;
	static int p,g,m;
	static void Main(){
		Sc sc=new Sc();
		int n=sc.I+1;
		sa=new Sa(sc.S,'1','9');
		var li=new List<int>();
		m=sa.sa.Length-1;
		p=m/n;
		g=n;
		if(m>p*n){g=m-p*n;p++;}
		for(int i = 0;i<sa.sa.Length;i++) {
			if(sa.sa[i]+p<sa.sa.Length){li.Add(sa.sa[i]);}
		}
		int lb=-1,ub=li.Count,mid=0;
		while(ub-lb>1){
			mid=(ub+lb)/2;
			if(Fu(li[mid])){ub=mid;}
			else{lb=mid;}
		}
		Console.WriteLine("{0}",sa.s.Substring(li[ub],p));
	}
	static bool Fu(int t){
		int z=0,i=0;
		while(z<g&&i<=m-p){
			bool bo=false;
			for(int j = 0;j<p;j++) {
				if(sa.s[i+j]<sa.s[t+j]){break;}
				if(sa.s[i+j]>sa.s[t+j]){bo=true;break;}
			}
			if(bo){i+=p-1;}
			else{i+=p;z++;}
		}
		return z==g;
	}
}
public class Sa{
	private readonly int n,m,o;
	public readonly string s;
	public readonly int[] sa;
	public Sa(string s,int a,int z){
		m=z-a+2;
		o=a-1;
		s+=(char)o;
		this.s=s;
		n=s.Length;
		int[] h=new int[n];
		var lms=new List<int>();
		int[] sub=new int[n];
		int[] hi=new int[m];
		int[] hc1=new int[m];
		int[] hc2=new int[m];
		int[] hc3=new int[m];
		hi[s[n-1]-o]=hc2[s[n-1]-o]=hc3[s[n-1]-o]=1;
		for(int i = n-2,k=n-1;i>=0;i--) {
			h[i]=s[i]!=s[i+1]?(s[i]>s[i+1]?1:0):h[i+1];
			hi[s[i]-o]++;
			if(h[i]==1&&h[i+1]==0){
				h[i+1]=2;
				lms.Add(i+1);
				sub[i+1]=k-i;
				k=i+1;
			}
		}
		for(int i = 1;i<m;i++) {
			hi[i]+=hi[i-1];
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		int c=lms.Count;
		sa=new int[n];
		for(int i = 0;i<c;i++) {
			hc2[s[lms[i]]-o]--;
			sa[hc2[s[lms[i]]-o]]=lms[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[hc1[s[sa[i]-1]-o]]=sa[i]-1;
				hc1[s[sa[i]-1]-o]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]-o]--;
				sa[hc3[s[sa[i]-1]-o]]=sa[i]-1;
			}
		}
		int[] lmsn=new int[c];
		for(int i = 0,j=c-1;i<n&&j>=0;i++) {
			if(h[sa[i]]==2){lmsn[j]=sa[i];j--;}
		}
		int[] lmsz=new int[n];
		int[] lmsc=new int[c];
		bool jf=false;
		int ki=0;
		for(int i = c-2;i>=0;i--) {
			if(sub[lmsn[i]]==sub[lmsn[i+1]]){
				bool bo=false;
				for(int j = 0;j<sub[lmsn[i]];j++) {if(s[lmsn[i]+j]!=s[lmsn[i+1]+j]){bo=true;break;}}
				if(bo){ki++;}
				else{jf=true;}
			}
			else{ki++;}
			lmsz[lmsn[i]]=ki;
		}
		for(int i = c-1;i>=0;i--) {lmsc[c-i-1]=lmsz[lms[i]];}
		hc2[0]=hc3[0]=hi[0];
		hc1[0]=0;
		for(int i = 1;i<m;i++) {
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		if(jf){
			lmsn=Fu2(lmsc,ki+1);
			for(int i = 0;i<c;i++) {lmsn[i]=lms[c-1-lmsn[i]];}
		}
		sa=new int[n];
		for(int i = 0;i<c;i++) {
			hc2[s[lmsn[i]]-o]--;
			sa[hc2[s[lmsn[i]]-o]]=lmsn[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[hc1[s[sa[i]-1]-o]]=sa[i]-1;
				hc1[s[sa[i]-1]-o]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]-o]--;
				sa[hc3[s[sa[i]-1]-o]]=sa[i]-1;
			}
		}
	}
	public int Fb(string t){return Bs1(t);}
	public Tuple<int,int> Ft(string t){
		int p=Bs1(t);
		return p==-1?Tuple.Create(-1,0):Tuple.Create(p,Bs2(t));
	}
	private int Bs1(string t){
		int l=t.Length-1;
		int lb=-1,mid=0,ub=n-1;
		while(ub-lb>1){
			mid=(ub+lb)/2;
			int ti=0;
			while(ti<l&&s[sa[mid]+ti]==t[ti]){ti++;}
			if(s[sa[mid]+ti]>=t[ti]){ub=mid;}
			else{lb=mid;}
		}
		bool bo=true;
		for(int i = 0;i<=l;i++) {if(s[sa[ub]+i]!=t[i]){bo=false;break;}}
		return bo?ub:-1;
	}
	private int Bs2(string t){
		int l=t.Length;
		int lb=-1,mid=0,ub=n;
		while(ub-lb>1){
			mid=(ub+lb)/2;
			int tm=Min(l,n-sa[mid])-1,ti=0;
			while(s[sa[mid]+ti]==t[ti]&&ti<tm){ti++;}
			if(s[sa[mid]+ti]>t[ti]){ub=mid;}
			else{lb=mid;}
		}
		return ub;
	}
	private int[] Fu2(IReadOnlyList<int> s,int m){
		int n=s.Count;
		var lms=new List<int>();
		int[] h=new int[n],sub=new int[n],sa=new int[n];
		int[] hi=new int[m],hc1=new int[m],hc2=new int[m],hc3=new int[m];
		hi[s[n-1]]=hc2[s[n-1]]=hc3[s[n-1]]=1;
		for(int i = n-2,k=n-1;i>=0;i--) {
			h[i]=s[i]!=s[i+1]?(s[i]>s[i+1]?1:0):h[i+1];
			hi[s[i]]++;
			if(h[i]==1&&h[i+1]==0){
				h[i+1]=2;
				lms.Add(i+1);
				sub[i+1]=k-i;
				k=i+1;
			}
		}
		int lm=lms.Count;
		for(int i = 1;i<m;i++) {
			hi[i]+=hi[i-1];
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		for(int i = 0;i<lm;i++) {
			hc2[s[lms[i]]]--;
			sa[hc2[s[lms[i]]]]=lms[i];
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[hc1[s[sa[i]-1]]]=sa[i]-1;
				hc1[s[sa[i]-1]]++;
			}
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]]--;
				sa[hc3[s[sa[i]-1]]]=sa[i]-1;
			}
		}
		int[] sl=new int[lm];
		for(int i = 0,j=lm-1;i<n&&j>=0;i++) {
			if(h[sa[i]]==2){sl[j]=sa[i];j--;}
		}
		int[] lmsz=new int[n];
		bool jf=false;
		int ki=0;
		for(int i = lm-2;i>=0;i--) {
			if(sub[sl[i]]==sub[sl[i+1]]){
				bool bo=false;
				for(int j = 0;j<sub[sl[i]];j++) {if(s[sl[i]+j]!=s[sl[i+1]+j]){bo=true;break;}}
				if(bo){ki++;}
				else{jf=true;}
			}
			else{ki++;}
			lmsz[sl[i]]=ki;
		}
		int[] lmsc=new int[lm];
		for(int i = lm-1;i>=0;i--) {lmsc[lm-i-1]=lmsz[lms[i]];}
		hc2[0]=hc3[0]=hi[0];
		hc1[0]=0;
		for(int i = 1;i<m;i++) {
			hc2[i]=hc3[i]=hi[i];
			hc1[i]=hi[i-1];
		}
		if(jf){
			sl=Fu2(lmsc,ki+1);
			for(int i = 0;i<lm;i++) {sl[i]=lms[lm-1-sl[i]];}
		}
		sa=new int[n];
		for(int i = 0;i<lm;i++) {
			hc2[s[sl[i]]]--;
			sa[n-1-hc2[s[sl[i]]]]=sl[i];
		}
		for(int i = n-1;i>=0;i--) {
			if(sa[i]>0&&h[sa[i]-1]==1){
				sa[n-1-hc1[s[sa[i]-1]]]=sa[i]-1;
				hc1[s[sa[i]-1]]++;
			}
		}
		for(int i = 0;i<n;i++) {
			if(sa[i]>0&&h[sa[i]-1]!=1){
				hc3[s[sa[i]-1]]--;
				sa[n-1-hc3[s[sa[i]-1]]]=sa[i]-1;
			}
		}
		return sa;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}