Game of the Rows CodeForces

Game of the Rows

Daenerys Targaryen has an army consisting of k groups of soldiers, thei-th group contains a_i soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane hasn rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats{1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.

A row in the airplane

Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.

Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.

Input

The first line contains two integers n andk (1 ≤ n ≤ 10000,1 ≤ k ≤ 100) — the number of rows and the number of groups of soldiers, respectively.

The second line contains k integers a₁, a₂, a₃, ..., a_k (1 ≤ a_i ≤ 10000), where a_i denotes the number of soldiers in thei-th group.

It is guaranteed that a₁ + a₂ + ... + a_k ≤ 8·n.

Output

If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).

You can choose the case (lower or upper) for each letter arbitrary.

Example

Input

2 25 8

Output

YES

Input

1 27 1

Output

NO

Input

1 24 4

Output

YES

Input

1 42 2 1 2

Output

YES

Note

In the first sample, Daenerys can place the soldiers like in the figure below:

In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.

In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.

In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).

详细题解：

这道题目找对方法其实不难，暴力解更容易想一些。

首先我们来说一下题意：这道题目大概是说有一个军队，军队里分为k个团，这k个团里有多少人需要你来输入。我们要实现将这几个团的人放入飞机并且这几个团之间的军人不能相邻。飞机一排有8个座位，分别为2，4，2；之间存在过道也属于不相邻，飞机共有n排。

思路：

军团入座时，我们尽量让人数多的团入座4人座，剩下的人入座2人座（刚开始入座的时候将所分配的4人、2人座均坐满）；坐满之后有时会发现还剩下有1人的军团，这时我们再向剩下的2人座入座，如果可以坐下则YES，不能则为NO。当入座4人座后，4人座未坐满，则这剩下空的4人座并入2人座进行分配。

下面附上AC代码：

#include<stdio.h>#include<iostream>using namespace std;int str[10005];int main(){int n,k,ans1,ans2;while(cin>>n>>k){for(int i=0;i<k;i++)cin>>str[i];ans1=n;ans2=2*n;for(int i=0;i<k;i++){int t=min(str[i]/4,ans1);ans1-=t;str[i]-=4*t;}ans2+=ans1;for(int i=0;i<k;i++){int t=min(str[i]/2,ans2);ans2-=t;str[i]-=2*t;}ans2+=ans1;for(int i=0;i<k;i++)ans2-=str[i];if(ans2>=0)cout<<"YES"<<endl;elsecout<<"NO"<<endl;}return 0;}