说明

一个$n$位数，每位可以是给出的$k$个数码中的一个数，可以有前导$0$,输出前$n/2$位之和与后$n/2$位之和相等的方案数，保证$n$是偶数。

输入的第一行是两个整数$n,k$，接下来的一行有$k$个数$d_1,d_2,\cdots,d_k(0\leq d_i\leq 9)$

输出一个数，为方案数模$998244353$的值

输入格式

The first line contains two integers $ n $ and $ k $ $ (2 \le n \le 2 \cdot 10^5, 1 \le k \le 10) $ — the number of digits in each ticket number, and the number of different decimal digits that may be used. $ n $ is even.

The second line contains a sequence of pairwise distinct integers $ d_1, d_2, \dots, d_k $ $ (0 \le d_i \le 9) $ — the digits that may be used in ticket numbers. The digits are given in arbitrary order.

输出格式

Print the number of lucky ticket numbers, taken modulo $ 998244353 $ .

样例

4 2
1 8

6

样例

20 1
6

1

样例

10 5
6 1 4 0 3

569725

样例

1000 7
5 4 0 1 8 3 2

460571165

提示

In the first example there are $ 6 $ lucky ticket numbers: $ 1111 $ , $ 1818 $ , $ 1881 $ , $ 8118 $ , $ 8181 $ and $ 8888 $ .

There is only one ticket number in the second example, it consists of $ 20 $ digits $ 6 $ . This ticket number is lucky, so the answer is $ 1 $ .