CodeForces 1011B

Description

Natasha is planning an expedition to Mars for $\mathrm{nn people.\; One\; of\; the\; important\; tasks\; is\; to\; provide\; food\; for\; each\; participant.}$

The warehouse has $\mathrm{mm daily\; food\; packages.\; Each\; package\; has\; some\; food\; type aiai.}$

Each participant must eat exactly one food package each day. Due to extreme loads, each participant must eat the same food type throughout the expedition. Different participants may eat different (or the same) types of food.

Formally, for each participant $\mathrm{jj Natasha\; should\; select\; his\; food\; type bjbj and\; each\; day jj-th\; participant\; will\; eat\; one\; food\; package\; of\; type bjbj.\; The\; values bjbj for\; different\; participants\; may\; be\; different.}$

What is the maximum possible number of days the expedition can last, following the requirements above?

Input

The first line contains two integers $\mathrm{nn and mm (1\le n\le 1001\le n\le 100, 1\le m\le 1001\le m\le 100) —\; the\; number\; of\; the\; expedition\; participants\; and\; the\; number\; of\; the\; daily\; food\; packages\; available.}$

The second line contains sequence of integers ${\mathrm{a1,a2,\dots ,ama1,a2,\dots ,am (1\le ai\le 1001\le ai\le 100),\; where aiai is\; the\; type\; of ii-th\; food\; package.}}^{}$

Output

Print the single integer — the number of days the expedition can last. If it is not possible to plan the expedition for even one day, print 0.

Sample Input

Input

4 10
1 5 2 1 1 1 2 5 7 2

Output

2

Input

100 1
1

Output

0

Input

2 5
5 4 3 2 1

Output

1

Input

3 9
42 42 42 42 42 42 42 42 42

Output

3

Hint

In the first example, Natasha can assign type $\mathrm{11 food\; to\; the\; first\; participant,\; the\; same\; type 11 to\; the\; second,\; type 55 to\; the\; third\; and\; type 22 to\; the\; fourth.\; In\; this\; case,\; the\; expedition\; can\; last\; for 22 days,\; since\; each\; participant\; can\; get\; two\; food\; packages\; of\; his\; food\; type\; (there\; will\; be\; used 44 packages\; of\; type 11,\; two\; packages\; of\; type 22 and\; two\; packages\; of\; type 55).}$

In the second example, there are $\mathrm{100100 participants\; and\; only 11 food\; package.\; In\; this\; case,\; the\; expedition\; can\text{'}t\; last\; even 11 day.}$

对存活天数进行暴力。

判断该天数能否成立的条件是，对水果的种类数进行暴力，判断所有的水果一共能支持多少人。

注意STL容器map 的使用。

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
#include<stack>
#include<deque>
#include<map>
#include<iostream>
using namespace std;
typedef long long  LL;
const double pi=acos(-1.0);
const double e=exp(1);
const int N = 100010;

#define lson i << 1,l,m
#define rson i << 1 | 1,m + 1,r

map<int,int> mp;
int main()
{
    int n,m,i,p,j;
    int x;
    scanf("%d%d",&n,&m);
    for(i=1;i<=m;i++)
    {
        scanf("%d",&x);
        mp[x]++;
    }
    if(m<n)
        printf("0
");
    else
    {
        p=m/n;
        map<int,int>::iterator it1;
        for(i=p;i>0;i--)
        {
            int sum=0;
            for(it1=mp.begin();it1!=mp.end();it1++)
            {
                sum+=it1->second/i;
            }
            if(sum>=n)
                break;
        }
        printf("%d
",i);
    }
    return 0;
}