Problem:
Score : 100 points

Problem Statement

You are given two strings s and t consisting of lowercase English letters and an integer L.

We will consider generating a string of length L by concatenating one or more copies of s and t. Here, it is allowed to use the same string more than once.

For example, when s = at, t = code and L = 6, the strings atatat, atcode and codeat can be generated.

Among the strings that can be generated in this way, find the lexicographically smallest one. In the cases given as input, it is always possible to generate a string of length L.

Constraints

1 ≤ L ≤ 2 × 10^5

1 ≤ |s|, |t| ≤ L

s and t consist of lowercase English letters.

It is possible to generate a string of length L in the way described in Problem Statement.

Input

Input is given from Standard Input in the following format:

N
x_1 s_1
x_2 s_2
:
x_N s_N

Output

Print the lexicographically smallest string among the ones that can be generated in the way described in Problem Statement.

Sample Input 1

6
at
code

Sample Output 1

atatat

This input corresponds to the example shown in Problem Statement.

Sample Input 2

8
coding
festival

Sample Output 2

festival

It is possible that either s or t cannot be used at all in generating a string of length L.

Sample Input 3

8
same
same

Sample Output 3

samesame

It is also possible that s = t.

Sample Input 4

10
coin
age

Sample Output 4

ageagecoin

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni();
		String s = ns(), t = ns();
		int x = s.length(), y = t.length();
		String can1 = null;
		for(int i = n/x;i >= 0;i--){
			if((n-i*x) % y == 0){
				StringBuilder sb = new StringBuilder();
				for(int k = 0;k < i;k++){
					sb.append(s);
				}
				for(int k = 0;k < (n-i*x)/y;k++){
					sb.append(t);
				}
				can1 = sb.toString();
				break;
			}
		}
		String can2 = null;
		for(int i = n/y;i >= 0;i--){
			if((n-i*y) % x == 0){
				StringBuilder sb = new StringBuilder();
				for(int k = 0;k < i;k++){
					sb.append(t);
				}
				for(int k = 0;k < (n-i*y)/x;k++){
					sb.append(s);
				}
				can2 = sb.toString();
				break;
			}
		}
		if(can1 == null){
			out.println(can2);
		}else if(can2 == null){
			out.println(can1);
		}else if(can1.compareTo(can2) < 0){
			out.println(can1);
		}else{
			out.println(can2);
		}
	}
	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private static char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}