#include <iostream>
#include <string>
#include <vector>

#include <atcoder/modint>
using namespace std;

using Mint = atcoder::modint998244353;
using Mat = vector<vector<Mint>>;

Mat mul(Mat a, Mat b)
{
    int N = a.size();
    Mat c(N, vector<Mint>(N, 0));
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            for (int k = 0; k < N; k++)
                c[i][k] += a[i][j] * b[j][k];
    return c;
}

Mat I(int N)
{
    Mat a(N, vector<Mint>(N, 0));
    for (int i = 0; i < N; i++)
        a[i][i] = 1;
    return a;
}

Mat pow(Mat a, int b)
{
    if (b == 0)
        return I(a.size());
    if (b == 1)
        return a;
    Mat r = pow(a, b / 2);
    r = mul(r, r);
    if (b & 1)
        r = mul(r, a);
    return r;
}

int main()
{
    string S;
    int K;
    cin >> S >> K;

    int HN = S.size() / 2;
    Mat M(HN + 1, vector<Mint>(HN + 1, 0));
    for (int i = 0; i <= HN; i++)
    {
        // curr diff: 2*i
        M[i][i] = HN * (HN - 1) + 2 * i * (HN - i);
        if (i != HN)
            M[i + 1][i] = (HN - i) * (HN - i);
        if (i != 0)
            M[i - 1][i] = i * i;
    }
    M = pow(M, K);

    Mat DP(1, vector<Mint>(1, 1));
    for (int i = 0; i < (int)S.size(); i++)
    {
        Mat N(i + 2, vector<Mint>(i + 2));
        // prefix sum = j, total difference = k
        for (int j = 0; j <= i; j++)
            for (int k = 0; k <= i; k++)
            {
                // choose '('
                {
                    int new_j = j + 1;
                    int new_k = k + (S[i] != '(');
                    if (new_j >= 0 && new_k >= 0)
                        N[new_j][new_k] += DP[j][k];
                }
                // choose ')'
                {
                    int new_j = j - 1;
                    int new_k = k + (S[i] != ')');
                    if (new_j >= 0 && new_k >= 0)
                        N[new_j][new_k] += DP[j][k];
                }
            }
        DP = N;
    }

    Mat C(HN + 1, vector<Mint>(HN + 1));
    for (int i = 0; i <= HN; i++)
    {
        C[i][i] = C[i][0] = 1;
        for (int j = 1; j < i; j++)
            C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
    }

    Mint ans = 0;
    for (int i = 0; i <= HN; i++)
        ans += M[i][0] * DP[0][2 * i] * (C[HN][i] * C[HN][i]).inv();
    cout << ans.val() << endl;
}