A12335. Lucky Tickets

All bus tickets in Berland have their numbers. A number consists of $n$ digits ( $n$ is even). Only $k$ decimal digits $d_1, d_2, \dots, d_k$ can be used to form ticket numbers. If $0$ is among these digits, then numbers may have leading zeroes. For example, if $n = 4$ and only digits $0$ and $4$ can be used, then $0000$ , $4004$ , $4440$ are valid ticket numbers, and $0002$ , $00$ , $44443$ are not.

A ticket is lucky if the sum of first $n / 2$ digits is equal to the sum of remaining $n / 2$ digits.

Calculate the number of different lucky tickets in Berland. Since the answer may be big, print it modulo $998244353$ .

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.

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

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 $1$ .