Game of the Rows

题意翻译

现在有 $K$ 个队，飞机有 $N$ 排座位，每排能坐 $8$ 个人，不同队伍的人不能坐相邻的位置。 相邻情况有 $5$ 种 $(1, 2), (3, 4), (4, 5), (5, 6), (7, 8)$。请问这 $n$ 排座位是否够坐。 （$K$ 个队的总人数小于 $8 \cdot N$） **【输入格式】** 每组数据共两行。 第一行包含两个数 $N,K$ 分别表示飞机有 $N$ 排座位，有 $K$ 个队伍（$1 \le n \le 10000$，$1 \le k \le 100$）。 第二行 有 $k$ 个数字，$a[1], \ldots, a[k]$，其中 $a[i]$ 表示第 $i$ 个队伍有 $a[i]$ 人。 其中 $a[1]+a[2]+ \cdots +a[K] \le 8 \cdot N$； **【输出格式】** 如果这 $n$ 排座位够坐，输出 `YES`，否则输出 `NO`。

题目描述

Daenerys Targaryen has an army consisting of $ k $ groups of soldiers, the $ i $ -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 has $ n $ 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 airplaneDaenerys 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.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1<=n<=10000 $ , $ 1<=k<=100 $ ) — the number of rows and the number of groups of soldiers, respectively. The second line contains $ k $ integers $ a_{1},a_{2},a_{3},...,a_{k} $ ( $ 1<=a_{i}<=10000 $ ), where $ a_{i} $ denotes the number of soldiers in the $ i $ -th group. It is guaranteed that $ a_{1}+a_{2}+...+a_{k}<=8·n $ .

输出格式

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.

输入输出样例

输入样例 #1

2 2
5 8

输出样例 #1

YES

输入样例 #2

1 2
7 1

输出样例 #2

NO

输入样例 #3

1 2
4 4

输出样例 #3

YES

输入样例 #4

1 4
2 2 1 2

输出样例 #4

YES

说明

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) $ .