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: Accepted)

#include "bits/stdc++.h"
using namespace std;

int main() {
	long long K, N;
	cin >> K >> N;
	if (K % 2 == 0) {
		cout << K / 2;
		for (int i = 1; i < N; i++) {
			cout << " " << K;
		}
		cout << endl;
		return 0;
	}
	stack<long long> ANS;
	long long Size = N;
	for (int i = 0; i < N; i++) ANS.push((K + 1) / 2);
	for (int i = 0; i < N / 2; i++) {
		if (ANS.top() == 1) ANS.pop(), Size--;
		else {
			ANS.top()--;
			for (int j = Size; j < N; j++) ANS.push(K);
			Size = N;
		}
	}
	vector<long long> ANS2;
	while (!ANS.empty()) ANS2.push_back(ANS.top()), ANS.pop();
	reverse(ANS2.begin(), ANS2.end());
	for (int i = 0; i < ANS2.size(); i++) {
		cout << ANS2[i];
		if (i == ANS2.size() - 1) cout << endl;
		else cout << " ";
	}
}