Problem:
Score : 800 points

Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.

Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

1 \leq N,K \leq 3 × 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

K N

Output

Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

Sample Input 1

3 2

Sample Output 1

2 1

There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).
The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

Sample Input 2

2 4

Sample Output 2

1 2 2 2

Sample Input 3

5 14

Sample Output 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define mem(a,b) memset(a,b,sizeof(a))
#define  For(i,a,b) for(int i=a,i##E=b;i<=i##E;++i)
#define rFor(i,a,b) for(int i=a,i##E=b;i>=i##E;--i)
typedef long long LL;
using namespace std;
const int N=300010;
template<typename T>inline bool chkmin(T &a,const T &b){return a>b?a=b,1:0;}
template<typename T>inline bool chkmax(T &a,const T &b){return a<b?a=b,1:0;}
template<typename T>inline void read(T &x)
{
	x=0;int _f(0);char ch=getchar();
	while(!isdigit(ch))_f|=(ch=='-'),ch=getchar();
	while( isdigit(ch))x=x*10+ch-'0',ch=getchar();
	x=_f?-x:x;
}
inline void file()
{
#ifdef ztzshiwo
	freopen("in.txt","r",stdin);
	freopen("out.txt","w",stdout);
#endif
}
int n,k,a[N];
int main()
{
	file();
	read(k),read(n);
	if(k&1)
	{
		For(i,1,n)a[i]=k/2+1;
		int x=n/2;
		while(x--)
		{
			int p=n;
			while(a[p]==0&&p)p--;
			a[p++]--;
			For(i,p,n)a[i]=k;
		}
		For(i,1,n)
		{
			if(!a[i])break;
			printf("%d ",a[i]);
		}
	}
	else
	{
		printf("%d ",k/2);
		For(i,2,n)printf("%d ",k);
	}
	return 0;
}