CodeForces 1011B

                                                 CodeForces 1011B

                               Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

                                                                               CodeForces 1011B

Description

Natasha is planning an expedition to Mars for n people. One of the important tasks is to provide food for each participant.

The warehouse has m daily food packages. Each package has some food type ai.

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 j Natasha should select his food type bj and each day j-th participant will eat one food package of type bj. The values bj 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 n and m (1≤n≤100, 1≤m≤100) — the number of the expedition participants and the number of the daily food packages available.

The second line contains sequence of integers a1,a2,…,am(1≤ai≤100), where ai is the type of i-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 1

food to the first participant, the same type 1 to the second, type 5 to the third and type 2 to the fourth. In this case, the expedition can last for 2 days, since each participant can get two food packages of his food type (there will be used 4 packages of type 1, two packages of type 2 and two packages of type 5).

In the second example, there are 100

participants and only 1 food package. In this case, the expedition can't last even 1 day.

 

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include <cstring>
#include<map>
using namespace std;
int main()
{
    map<int,int> p;
    int n,m;
    int i,j,k;
    cin>>n>>m;
    for(i=0;i<m;i++)
    {
        int t;
        cin>>t;
        p[t]++;
    }
    if(n>m)
        cout<<"0"<<endl;
    else
    {
        for(i=1;;i++)
        {
            int s=0;
            map<int,int>::iterator it;
            for(it=p.begin();it!=p.end();it++)
            {
                s+=(it->second)/i;
            }
            if(s<n)
                break;
        }
        cout<<i-1<<endl;
    }
    return 0;
}