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<cstdio>
using namespace std;
int n,l,a[300010],i,t,m;
int main()
{
	scanf("%d%d",&n,&l);
	if (n%2==0)
	{
		printf("%d ",n/2);
		for (i=2;i<=l;i++) printf("%d ",n);
		return 0;
	}
	t=(l-1)/2;
	m=n/2+1;
	for (i=1;i<=l;i++) a[i]=m;
	while (t--)
	{
		int k=l;
		while (a[k]==0) k--;
		a[k]--;
		//a[k+1]=m;
		for (i=k+1;i<=l;i++) a[i]=m;
		//for (i=1;i<=l;i++) printf("%d ",a[i]);
		//printf("\n");
	}
	for (i=1;i<=l;i++) 
	{
		if (a[i]!=0) printf("%d ",a[i]);
		else break;
	} 
}