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.

Examples

Input

3 2


Output

2 1


Input

2 4


Output

1 2 2 2


Input

5 14


Output

3 3 3 3 3 3 3 3 3 3 3 3 2 2
//2017-11-5
//miaomiao
//
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

#define pb push_back
#define ppb pop_back
#define For(i, a, b) for(int i = (a); i <= (int)(b); ++i)

#define N (300000+5)

vector<int> ans;

int main(){	
	int k, n;
	scanf("%d%d", &k, &n);
	
	if(!(k&1)){
		printf("%d", k/2);
		For(i, 2, n) printf(" %d", k);
		return 0;
	}
	
	For(i, 1, n) ans.pb((k+1)/2);
	int nn = n / 2;

	while(nn--){
		if(ans.back() == 1) ans.ppb();
		else{
			--ans.back();
			For(i, ans.size()+1, n) ans.pb(k);
		}
	}

	For(i, 0, ans.size()-1) printf("%d%c", ans[i], i==((int)ans.size()-1)? '\n': ' ');

	return 0;
}