Codeforces_768_D_(概率dp)

D. Jon and Orbs

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Jon Snow is on the lookout for some orbs required to defeat the white walkers. There are k different types of orbs and he needs at least one of each. One orb spawns daily at the base of a Weirwood tree north of the wall. The probability of this orb being of any kind is equal. As the north of wall is full of dangers, he wants to know the minimum number of days he should wait before sending a ranger to collect the orbs such that the probability of him getting at least one of each kind of orb is at least , where ε < 10 - 7.

To better prepare himself, he wants to know the answer for q different values of pi. Since he is busy designing the battle strategy with Sam, he asks you for your help.

Input

First line consists of two space separated integers k, q (1 ≤ k, q ≤ 1000) — number of different kinds of orbs and number of queries respectively.

Each of the next q lines contain a single integer pi (1 ≤ pi ≤ 1000) — i-th query.

Output

Output q lines. On i-th of them output single integer — answer for i-th query.

Examples

input

1 1
1

output

1

input

2 2
1
2

output

2
2

 题意：有k种球，每天可得到一个球，其种类是任意一种，问每种球至少有一个的概率至少为 (p<1000)需要几天。

自己只想到用概率去算，但是也不知对不对，几乎没有思路，于是看了官方题解。

思路：dp[i][j]:第i天有j种的概率。那么可以有dp[i][j]=dp[i-1][j]*(j/k)+dp[i-1][j-1]*(k-j+1)/k;

看了题解觉得很容易，但是自己却想不到啊。。。。。。。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
#define N 10005
double dp[N][1005];

int main()
{
    int k,q;
    scanf("%d%d",&k,&q);
    dp[1][1]=1;
    for(int i=2; i<N; i++)
        for(int j=1; j<=k; j++)
            dp[i][j]=dp[i-1][j]*((double)j/k)+dp[i-1][j-1]*((double)(k-j+1)/k);
    while(q--)
    {
        double p;
        scanf("%lf",&p);
        int i;
        for(i=1; i<N; i++)
            if(dp[i][k]>=(p/2000))
                break;
        printf("%d
",i);
    }
    return 0;
}