Codeforces Round #407 (Div. 2) E The Great Mixing（BFS）

Sasha and Kolya decided to get drunk with Coke, again. This time they have k types of Coke. i-th type is characterised by its carbon dioxide concentration . Today, on the party in honour of Sergiy of Vancouver they decided to prepare a glass of Coke with carbon dioxide concentration . The drink should also be tasty, so the glass can contain only integer number of liters of each Coke type (some types can be not presented in the glass). Also, they want to minimize the total volume of Coke in the glass.

Carbon dioxide concentration is defined as the volume of carbone dioxide in the Coke divided by the total volume of Coke. When you mix two Cokes, the volume of carbon dioxide sums up, and the total volume of Coke sums up as well.

Help them, find the minimal natural number of liters needed to create a glass with carbon dioxide concentration . Assume that the friends have unlimited amount of each Coke type.

Input

The first line contains two integers n, k (0 ≤ n ≤ 1000, 1 ≤ k ≤ 10⁶) — carbon dioxide concentration the friends want and the number of Coke types.

The second line contains k integers a₁, a₂, ..., a_k (0 ≤ a_i ≤ 1000) — carbon dioxide concentration of each type of Coke. Some Coke types can have same concentration.

Output

Print the minimal natural number of liter needed to prepare a glass with carbon dioxide concentration , or -1 if it is impossible.

Examples

Input

400 4
100 300 450 500

Output

2

Input

50 2
100 25

Output

3

Note

In the first sample case, we can achieve concentration using one liter of Coke of types and : .

In the second case, we can achieve concentration using two liters of type and one liter of type: .

题意：给你一些无限量不同浓度的二氧化碳，然后让你配出固定浓度为k的二氧化碳，问最少需要多少不同浓度的二氧化碳？

思路：假设需要m个不同浓度的二氧化碳则m满足

初始化x=0，求出下一次x=0时就得到了最后结果。

#include <iostream>
#include<cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <map>
using namespace std;
queue<int>que;
int a[1000005];
map<int,int>mp;
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    for(int i=0; i<m; i++)
    {
        scanf("%d",&a[i]);
        a[i]=a[i]-n;
    }
    sort(a,a+m);
    int cnt=unique(a,a+m)-a;
    que.push(0);
    while(!que.empty())
    {
        int x=que.front();
        que.pop();
        for(int i=0; i<cnt; i++)
        {
            int y=a[i]+x;
            if(abs(y)>=1001) continue;
            if(y==0)
            {
                printf("%d
",mp[x]+1);
                return 0;
            }
            if(!mp[y])
            {
                mp[y]=mp[x]+1;
                que.push(y);
            }
        }
    }
    printf("-1
");
    return 0;
}

知识点：1.STL中unique是去重函数，2.在BFS的过程中使用map数组进行标记。