[codeforces1158B]The minimal unique substring

Copyright: hard code word, when you reprint remember to tell me https://blog.csdn.net/dxyinme/article/details/90489958

time limit per test : 1 second
memory limit per test : 256 megabytes

Let s be some string consisting of symbols “0” or “1”. Let’s call a string t a substring of string s, if there exists such number $1≤l≤|s|−|t|+1$ that $t=s_ls_{l+1}…s_{l+|t|−1}$. Let’s call a substring $t$ of string $s$ unique, if there exist only one such $l$.

For example, let $s$=“1010111”. A string $t$=“010” is an unique substring of $s$, because $l$=2 is the only one suitable number. But, for example t=“10” isn’t a unique substring of $s$, because $l$=1 and $l$=3 are suitable. And for example $t$=“00” at all isn’t a substring of $s$, because there is no suitable $l$.

Today Vasya solved the following problem at the informatics lesson: given a string consisting of symbols “0” and “1”, the task is to find the length of its minimal unique substring. He has written a solution to this problem and wants to test it. He is asking you to help him.

You are given 2 positive integers $n$ and $k$, such that $(n$ $mod$ $2)=(k$ $mod$ $2)$, where $(x$ $mod$ $2)$ is operation of taking remainder of x by dividing on 2. Find any string s consisting of n symbols “0” or “1”, such that the length of its minimal unique substring is equal to $k$.

Input

The first line contains two integers $n$ and $k$, separated by spaces $(1≤k≤n≤100000, (k$ $mod$ $2)=(n$ $mod$ $2))$.

Output

Print a string $s$ of length $n$, consisting of symbols “0” and “1”. Minimal length of the unique substring of $s$ should be equal to $k$. You can find any suitable string. It is guaranteed, that there exists at least one such string.

Examples
Input

4 4

Output

1111

Input

5 3

Output

01010

Input

7 3

Output

1011011

Note

In the first test, it’s easy to see, that the only unique substring of string s=“1111” is all string s, which has length 4.

In the second test a string s=“01010” has minimal unique substring t=“101”, which has length 3.

In the third test a string s=“1011011” has minimal unique substring t=“110”, which has length 3.

Meaning of the questions:
given two numbers $n,k$ , they are the same parity, a configuration required length $n$ of the string 01 $s$ , such that $s$ all length of less than $k$ of the substring $s$ are more than once. Ensure solvable.

Solution:
First we set $l=(n-k)/2$
because the solution must exist, and is necessarily $s_{l+1}...s_{n-l}$
Then the rest is well understood, so lets divided as follows $1$ to $k-1$ length of the string are duplicated.
As long as each of us $((n-k)/2+1)*q (q>=n)$ at the other locations are placed in a 0 to 1.

#include<bits/stdc++.h>
#define LiangJiaJun main
using namespace std;
int n,k;
int LiangJiaJun(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++){
		printf("%d",(i%((n-k)/2+1)>0));
	}
	puts("");
	return 0;
}