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 rep(i,a,b) for (int i=(a); i<=(b); i++)
using namespace std;

const int maxn = 300005;
int a[maxn], top, n, K;

int main() {
	scanf("%d%d", &K, &n);
	if (!(K&1)) {
		printf("%d ", K / 2);
		rep (i, 2, n) printf("%d ", K / 2 + 1);
		return 0;
	}
	rep (i, 1, n) a[i] = (K + 1) / 2;
	top = n;
	rep (i, 1, n / 2)
		if (a[top] == 1) top--;
		else {
			a[top]--;
			while (top < n) a[++top] = K;
		}
	rep (i, 1, top) printf("%d ", a[i]);
	
	return 0;
}