Superfactorial numeral system

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시간 제한1초메모리 제한1024 MB

요약

유리수 p/q를 a1 + a2/2! + a3/3! + ... 형태의 혼합 진법 표현으로 나타내되, k >= 2에 대해 0 <= ak < k를 만족하고 끝의 0은 생략한다.

난이도: 보통10점 중 5점
유형: 수학, 정수론, 그리디, 구현
정답자: 아직 제출이 없습니다

문제

On the most perfect of all planets i1c5l various numeral systems are being used during programming contests. In the second division they use a superfactorial numeral system. In this system any positive integer is presented as a linear combination of numbers converse to factorials:

$\frac{p}{q} = a\_1 + \frac{a\_2}{2!} + \frac{a\_3}{3!} + \ldots + \frac{a\_n}{n!}\\,.$

Here $a\_1$ is non-negative integer, and integers $a\_k$ for $k \ge 2$ satisfy $0 \le a\_k < k$ . The nonsignificant zeros in the tail of the superfactorial number designation $\frac{p}{q}$ are rejected. The task is to find out how the rational number $\frac{p}{q}$ is presented in the superfactorial numeral system.

입력

Single line contains two space-separated integers $p$ and $q$ ( $1 \le p \le 10^6$ , $1 \le q \le 10^6$ ).

출력

Single line should contain a sequence of space-separated integers $a\_1, a\_2, \ldots, a\_n$ , forming a number designation $\frac{p}{q}$ in the superfactorial numeral system. If several solution exist, output any of them.

예제3

예제 1
입력
```
1 2
```
예상 출력
```
0 1
```
예제 2
입력
```
2 10
```
예상 출력
```
0 0 1 0 4
```
예제 3
입력
```
10 2
```
예상 출력
```
5
```