import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    return (g1[n] * g2[r] % mod) * g2[n-r] % mod

mod = 998244353
N = 2*10**5
g1 = [1]*(N+1)
g2 = [1]*(N+1)
inverse = [1]*(N+1)

for i in range( 2, N + 1 ):
    g1[i]=( ( g1[i-1] * i ) % mod )
    inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[0]=0

def poly_eval(f,x):
    res = 0
    for i in range(len(f)):
        res += f[i] * pow(x,i)
    return res

def add(f,g):
    res = [0 for i in range(max(len(f),len(g)))]
    for i in range(len(f)):
        res[i] += f[i]
    for j in range(len(g)):
        res[j] += g[j]
    return res

def mul(f,g):
    res = [0 for i in range(len(f)+len(g)-1)]
    for i in range(len(f)):
        for j in range(len(g)):
            res[i+j] += f[i] * g[j]
    return res

def mat_mul(X,Y):
    n,m = len(X),len(Y[0])
    res = [[0 for j in range(m)] for i in range(n)]
    for i in range(n):
        for j in range(m):
            for k in range(len(Y)):
                res[i][j] += X[i][k] * Y[k][j]
                res[i][j] %= mod
    return res

S = input()
K = int(input())
n = len(S)//2

left = set([i for i in range(2*n) if S[i]=="("])
right = set([i for i in range(2*n) if S[i]==")"])

dp = [[0 for k in range(n+1)] for j in range(n+1)]
dp[0][0] = 1
for i in range(2*n):
    ndp = [[0 for k in range(n+1)] for j in range(n+1)]
    for j in range(n+1):
        for k in range(n+1):
            if not dp[j][k]:
                continue

            """
            (にする
            """
            if i not in left and j < n and k < n:
                ndp[j+1][k+1] += dp[j][k]
                ndp[j+1][k+1] %= mod
            elif j < n:
                ndp[j+1][k] += dp[j][k]
                ndp[j+1][k] %= mod
            
            """
            )にする
            """
            if j!=0:
                ndp[j-1][k] += dp[j][k]
                ndp[j-1][k] %= mod
    
    dp = ndp

A = [[0 for j in range(n+1)] for i in range(n+1)]
for i in range(n+1):
    if i!=0:
        A[i-1][i] = i*i
    A[i][i] = 2*i*(n-i) + n*(n-1)
    if i!=n:
        A[i+1][i] = (n-i)*(n-i)

E = [[dp[0][i]] for i in range(n+1)]
while K:
    if K&1:
        E = mat_mul(A,E)
    A = mat_mul(A,A)
    K >>= 1

print(E[0][0])