2016 Personal Training #5 Div.2 Gym 100637J

C - 寅

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

standard input/output 
Statements

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:

Here a₁ is non-negative integer, and integers a_k for k ≥ 2 satisfy 0 ≤ a_k < k. The nonsignificant zeros in the tail of the superfactorial number designation  are rejected. The task is to find out how the rational number  is presented in the superfactorial numeral system.

Input

Single line contains two space-separated integers p and q (1 ≤ p ≤ 10⁶, 1 ≤ q ≤ 10⁶).

Output

Single line should contain a sequence of space-separated integers a₁, a₂, ..., a_n, forming a number designation  in the superfactorial numeral system. If several solution exist, output any of them.

Sample Input

Input

1 2

Output

0 1 

Input

2 10

Output

0 0 1 0 4 

Input

10 2

Output

5 

唉，弄半天真是貪心，當時錯兩邊就沒再仔細看，倒是卡在數據類型半天。

題意：給你p，q輸出滿足公式的ai，

思路：從a1開始，a2=p*2!/q，...;直到p爲零結束。有個小疑問0<=ak<k這個條件好像沒什麼用？難道其中有什麼...。

代碼如下：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
#define INF 0x3f3f3f3f
int main()
{
  LL p,q;
  scanf("%lld%lld",&p,&q);
  for(int i=2;;i++)
  {
    int ans=p/q;
    if(ans>=i&&i!=2)
    {
      ans=i-1;
    }
    p=(p-ans*q)*i;
    printf("%d",ans);
    if(p==0)
    {
      printf("\n");break;
    }
    printf(" ");
  }
}