p03561 AtCoder Regular Contest 084 - Finite Encyclopedia of Integer Sequences
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
```python
import sys
input = sys.stdin.readline

K,N = map(int,input().split())

if K % 2 == 0:
    L = K // 2
    R = L + 1
    # 先頭の文字が L のものの最後、R のものの最初、で境界
    arr = [L] + [K] * (N-1)
else:
    """
    [3,3,3,3,3] だと 手前に3 33 333 3333 が余分。2歩戻る。
    """
    arr = [(K+1)//2] * N
    x = N//2# x歩 戻る
    for i in range(x):
        arr[-1] -= 1
        if arr[-1] == 0:
            arr.pop()
            continue
        L = len(arr)
        if L < N:
            arr += [K] * (N-L)

answer = ' '.join(map(str,arr))
print(answer)
```