#include <bits/stdc++.h>
using namespace std;

constexpr int mod = 998244353;

int dp[201][201][201];

long long tmp1[201],tmp2[201];

long long modpow(long long a,long long b) {
    long long ans = 1;
    while(b) {
        if(b & 1) {
            (ans *= a) %= mod;
        }
        (a *= a) %= mod;
        b /= 2;
    }
    return ans;
}

vector<vector<long long>> Mul(vector<vector<long long>> A,vector<vector<long long>> B) {
    vector<vector<long long>>ans(A.size(),vector<long long>(A.size()));
    for(int i = 0; i < A.size(); i++) {
        for(int j = 0; j < A.size(); j++) {
            for(int k = 0; k < A.size(); k++) {
                ans[i][j] += A[i][k]*B[k][j]%mod;
                ans[i][j] %= mod;
            }
        }
    }
    return ans;
}

vector<vector<long long>> Pow(vector<vector<long long>> A,long long B) {
    vector<vector<long long>>ans(A.size(),vector<long long>(A.size()));
    ans[0][0] = 1;
    while (B) {
        if(1 & B) {
            ans = Mul(ans,A);
        }
        A = Mul(A,A);
        B /= 2;
    }
    return ans;
}

long long fac[200005], finv[200005], inv[200005];

void COMinit() {
    fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;
    for (int i = 2; i < 200005; i++) {
        fac[i] = fac[i - 1] * i % mod;
        inv[i] = mod - inv[mod % i] * (mod / i) % mod;
        finv[i] = finv[i - 1] * inv[i] % mod;
    }
}

long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
}

long long COM2(int K) {
    return tmp1[K]*modpow(tmp2[K],mod-2)%mod;
}

void modplus(int &x,int y) {
    x += y;
    if(x >= mod) x -= mod;
}

int main() {
    string S;
    int K;
    cin >> S >> K;
    int N = (int)S.size();
    dp[0][0][0] = 1;
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            for(int k = 0; k < N; k++) {
                int f = ('(' != S[i]);
                modplus(dp[i+1][j+1][k+f],dp[i][j][k]);
                f ^= 1;
                modplus(dp[i+1][j-1][k+f],dp[i][j][k]);
            }
        }
    }
    tmp1[0] = K;
    for(int i = K-1; i >= K-N; i--) {
        tmp1[K-i] = tmp1[K-i-1]*max(1,i)%mod;
    }
    tmp2[0] = 1;
    for(int i = 1; i <= N; i++) {
        tmp2[i] = tmp2[i-1]*i%mod;
    }
    vector<vector<long long>>A(N/2+1,vector<long long>(N/2+1));
    for(int i = 0; i <= N/2; i++) {
        A[i][i] = N/2*(N-1)-i*i-(N/2-i)*(N/2-i);
        if(i+1 <= N/2) {
            A[i][i+1] = (N/2-i)*(N/2-i);
        }
        if(i) {
            A[i][i-1] = i*i;
        }
    }
    A = Pow(A,K);
    COMinit();
    int ans = 0;
    for(int i = 0; i <= N; i += 2) {
        modplus(ans,COM2(i/2)*dp[N][0][i]%mod*modpow(COM(N/2,i/2)*COM(N/2,i/2)%mod,mod-2)%mod*A[0][i/2]%mod);
    }
    cout << ans << endl;
}