Coderforce 499 B. Planning The Expedition（二分）

题意：

                                                                           B. Planning The Expedition

time limit per test 1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

The warehouse has 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 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 nn and mm (1≤n≤1001≤n≤100, 1≤m≤1001≤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,…,ama1,a2,…,am (1≤ai≤1001≤ai≤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.

Examples

input

Copy

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

output

Copy

2

input

Copy

100 1
1

output

Copy

0

input

Copy

2 5
5 4 3 2 1

output

Copy

1

input

Copy

3 9
42 42 42 42 42 42 42 42 42

output

Copy

3

Note

In the first example, Natasha can assign type 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 100100 participants and only 11 food package. In this case, the expedition can't last even 11 day.

大意：n个人，m个食品，一个人必须吃同样价值的食物，一天一个。问最多能够n个人吃多少天？

解题总结：倒推过去，假设吃x天，看满不满足，就是个二分。二分情况注意一下，最大值设定的要比数据最大值大，mid=l/r,我推荐，还有l<r-1,也是避免0的时候出错，很有必要

AC代码：

#include<bits/stdc++.h>
using namespace std;
int n,m,h[101];
bool camp(int x,int y){
	return x>y;
}
bool check(int x){
	int cnt=0;
	for(int i=0;i<=100;i++){
		cnt+=h[i]/x;
		if(h[i]<x)break;
	}
	return cnt>=n;
}
int main(){
    ios::sync_with_stdio(false);
    cin>>n>>m;
    for(int i=1;i<=m;i++){
    	int ip;cin>>ip;
    	h[ip]++;
	}	
	sort(h,h+101,camp);
	int l=0,r=100+m;
	while(l<r-1){
		int mid=(r+l)/2;
		if(check(mid))l=mid;
		else r=mid;
	}
	cout<<l<<endl;
	return 0;
}