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>
using namespace std;

using ll = long long;

const int N = 300005;
const ll inf = ll(1e12);

int n, k;
ll b[N];

int main(){
    scanf("%d%d", &n, &k);
    if(~n & 1){
        printf("%d ", n / 2);
        for(int i = 0; i < k - 1; i++) printf("%d ", n / 2 + 1);
        return 0;
    }
    int o = k & 1;
    b[k] = 1;
    for(int i = k - 1; i >= 1; i--) b[i] = min(inf, b[i + 1] * n + 1);
    for(int i = 1; i <= k; i++){
        if(~(k - i) & 1) o--;
        int t = (n + 1) / 2;
        while(o > b[i] / 2){ o -= b[i]; t++; }
        while(o < -((b[i] - 1) / 2)){ o += b[i]; t--; }
        if(!t) break;
        printf("%d ", t);
    }
}