Gray code P5657

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Title Description

Typically, people are accustomed to all the  n- n-bit binary string as lexicographic order, for example, all the 2-bit binary strings are lexicographically in ascending order are: 00,01,10,11.

Gray code (Gray Code) is a special  n- n-bit binary string permutation method, which requires between two binary strings exactly adjacent to a different, in particular, a first string and a string to be regarded as the last adjacent .

All 2-bit binary strings are arranged in a gray code example is: 00,01,11,10.

n- n-bit Gray code is more than one algorithm is given below wherein generating Gray code:

1. A Gray code of a binary string composed of two, in order: 0,1.
2. n-+. 1 n- + . 1-bit Gray code before  2 ^ n- 2 n-binary string or so the algorithm generated by the  n- n-bit Gray code (a total of  2 ^ n- 2 n-a  n- n-bit binary string) are arranged in order, and then before each string composed of 0 and a prefix.
3. n-+. 1 n- + After a Gray code  2 ^ n- 2 n-binary string, it may be formed so algorithm generates  n- n-bit Gray code (a total of  2 ^ n- 2 n-a  n- n-bit binary string) in reverse order, and then before each string constituting a prefix 1.

In summary, n-1 + n- + 1-bit Gray code, the  n- n-bit Gray code  2 ^ n- 2 are arranged in order prefix plus 0 n binary string, and in reverse order plus a prefix composed of a total of  2 ^ { } +. 1 n- 2 n- + . 1 binary string. Further, the  n- n-bit Gray code in  2 ^ n- 2 n-binary strings, the order of the above-described algorithm we get them from  0 \ 2 ^ n-SIM -. 1 0 ~ 2 n- - . 1 ID.

According to the algorithm, two Gray code can launch this:

1. Gray code is known as a 0.
2. The first two Gray code to 00, 01. After two Gray code is 11,10. Were combined to give 00,01,11,10, numbered sequentially from 0 to 3.

Similarly, three Gray code can launch this:

1. Gray code is known as 2: 00,01,11,10.
2. The first four Gray code is: 000,001,011,010. After four Gray code is: 110,111,101,100. Combined to give: 000,001,011,010,110,111,101,100, sequentially numbered from 0 to 7.

Now given  n- n-, K K, you obtain the above-described algorithm for generating the  n- n-bit Gray code in  K K number of binary string.

Input Format

Only one line two integers  the n- the n-, k k, meaning see title description.

Output Format

Only a row of  the n- the n-bit binary string represents the answer.

Sample input and output

Input # 1copy

2 3

Output # 1copy

10

Input # 2copy

3 5

Output # 2copy

111

Input # 3copy

44 1145141919810

Output # 3copy

00011000111111010000001001001000000001100011

Description / Tips

Sample 1 [explain]

Gray code 2: 00,01,11,10, numbered from 0~3, string 3 is therefore 10.

Sample 2 [explain]

3 Gray code: 000,001,011,010,110,111,101,100, numbered from 0 to 7, so the string 5 is 111.

【data range】

For  50 \% . 5 0 % Data: n-\ Leq 10 n- ≤ . 1 0

For  80 \% . 8 0 % Data: K \ Leq. 5 \ ^. 6 Times 10 K ≤ . 5 × . 1 0 . 6

For  95 \% . 9 . 5 % of the data: K \ Leq 63 is {2} ^ -. 1 K ≤ 2 . 6 . 3 - . 1

For  100 \% . 1 0 0 % data: . 1 \ n-Leq \ Leq 64 . 1 ≤ n- ≤ . 6 . 4,  0 \ Leq K \ ^ lt n-2 0 ≤ K < 2 n-

 

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
unsigned long long maxx=1;
int n,where=1;
bool ok;
unsigned long long k;
bool a[10000];
int main () {
	cin>>n>>k;
	for(int i=1;i<n;i++){
		maxx*=2;
	}
	ok=1;
	while(maxx>0){
		if(ok==1){
			//cout<<maxx<<"   "<<k<<endl;
			if(maxx>k){
				a[where++]=0;
			}
			else{
				k-=maxx;
				a[where++]=1;
				ok=0;
			}
			maxx/=2;
			continue;
		}
		if(ok==0){
			//cout<<maxx<<"   "<<k<<endl;
			if(maxx>k){
				a[where++]=1;
				ok=1;
			}
			else{
				k-=maxx;
				a[where++]=0;
			}
			maxx/=2;
			continue;
		}
	}
	for(int i=1;i<=n;i++){
		printf("%d",a[i]);
	}
	return 0;
}