CF57E.Chess

Brian the Rabbit adores chess. Not long ago he argued with Stewie the Rabbit that a knight is better than a king. To prove his point he tries to show that the knight is very fast but Stewie doesn't accept statements without evidence. He constructed an infinite chessboard for Brian, where he deleted several squares to add some more interest to the game. Brian only needs to count how many different board squares a knight standing on a square with coordinates of (0, 0) can reach in no more than k moves. Naturally, it is forbidden to move to the deleted squares.

Brian doesn't very much like exact sciences himself and is not acquainted with programming, that's why he will hardly be able to get ahead of Stewie who has already started solving the problem. Help Brian to solve the problem faster than Stewie.

兔子布莱恩酷爱国际象棋。不久前，他与兔子斯图威争论：马比王更优秀。为了证明自己的观点，他试图说明马的移动速度非常快；但斯图威不接受没有证据的论断。于是，他为布莱恩构造了一块无限大的棋盘，并从中删去了若干格子，以增加游戏的趣味性。现在，布莱恩只需计算：一只位于坐标 $(0,\,0)$ 处的马，在至多 $k$ 步内能够到达多少个不同的棋盘格子。当然，禁止移动到已被删除的格子上。

布莱恩本人并不太喜欢严谨科学，也不懂编程，因此他几乎不可能赶在已开始解题的斯图威之前得出答案。请帮助布莱恩比斯图威更快地解决这个问题。

The first line contains two integers k and n (0 ≤ k ≤ 1018, 0 ≤ n ≤ 440) which are correspondingly the maximal number of moves a knight can make and the number of deleted cells. Then follow n lines, each giving the coordinates of a deleted square in the form (x__i, y__i) (|x__i| ≤ 10, |y__i| ≤ 10). All the numbers are integer, the deleted squares are different and it is guaranteed that the square (0, 0) is not deleted.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).

第一行包含两个整数 $k$ 和 $n$（$0 \le k \le 10^{18}$，$0 \le n \le 440$），分别表示骑士最多可移动的步数以及被删除的格子数量。接下来是 $n$ 行，每行以 $(x_i,\,y_i)$ 的形式给出一个被删除的方格的坐标（满足 $|x_i| \le 10$，$|y_i| \le 10$）。所有数字均为整数，被删除的方格互不相同，且保证方格 $(0,\,0)$ 未被删除。

请注意：在 C++ 中读写 64 位整数时，请勿使用 %lld 格式说明符；推荐使用 cin（也可使用 %I64d）。

You must print the answer on a single line. As it can be rather long, you should print it modulo 1000000007.

你必须在一行内输出答案。由于答案可能很长，你需要输出其对 $1000000007$ 取模的结果。