human
Can you provide a Python code to print the number of lucky ticket numbers, taken modulo 998244353 given the following:
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, ..., 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.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 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, ..., d_k (0 ≤ d_i ≤ 9) — the digits that may be used in ticket numbers. The digits are given in arbitrary order.

Output

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

Examples

Input

4 2
1 8

Output

6

Input

20 1
6

Output

1

Input

10 5
6 1 4 0 3

Output

569725

Input

1000 7
5 4 0 1 8 3 2

Output

460571165

Note

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.
#!/us
assistant
#Here is Python code to print the number of lucky ticket numbers, taken modulo 998244353.
r/bin/env python2
"""
This file is part of https://github.com/cheran-senthil/PyRival
Copyright 2019 Cheran Senthilkumar <hello@cheran.io>

"""
from __future__ import division, print_function

import itertools
import math
import os
import sys
from atexit import register
from io import BytesIO

class dict(dict):
    """dict() -> new empty dictionary"""

    def items(self):
        """D.items() -> a set-like object providing a view on D's items"""
        return dict.iteritems(self)

    def keys(self):
        """D.keys() -> a set-like object providing a view on D's keys"""
        return dict.iterkeys(self)

    def values(self):
        """D.values() -> an object providing a view on D's values"""
        return dict.itervalues(self)

def gcd(x, y):
    """greatest common divisor of x and y"""
    while y:
        x, y = y, x % y
    return x

range = xrange

filter = itertools.ifilter
map = itertools.imap
zip = itertools.izip

sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
sys.stdout = BytesIO()
register(lambda: os.write(1, sys.stdout.getvalue()))

input = lambda: sys.stdin.readline().rstrip('\r\n')

MOD = 998244353
MODF = float(MOD)
SHRT = float(1 << 16)
ROOT = 3.0

fmod = lambda x: x - MODF * math.trunc(x / MODF)
fmul = lambda a, b: fmod(math.trunc(a / SHRT) * fmod(b * SHRT) + (a - SHRT * math.trunc(a / SHRT)) * b)

def fpow(x, y):
    res = 1.0
    while y > 0:
        if y & 1 == 1:
            res = fmul(res, x)
        if y > 1:
            x = fmul(x, x)
        y >>= 1

    return res

def ntt(a, inv=False):
    n = len(a)
    w = [1.0] * (n >> 1)

    w[1] = fpow(ROOT, (MOD - 1) // n)
    if inv:
        w[1] = fpow(w[1], MOD - 2)

    for i in range(2, (n >> 1)):
        w[i] = fmul(w[i - 1], w[1])

    rev = [0] * n
    for i in range(n):
        rev[i] = rev[i >> 1] >> 1
        if i & 1 == 1:
            rev[i] |= (n >> 1)
        if i < rev[i]:
            a[i], a[rev[i]] = a[rev[i]], a[i]

    step = 2
    while step <= n:
        half, diff = step >> 1, n // step
        for i in...