#include <bits/stdc++.h>
using namespace std;
const long long MOD = 998244353;
long long modpow(long long a, long long b){
	long long ans = 1;
	while (b > 0){
		if (b % 2 == 1){
			ans *= a;
			ans %= MOD;
		}
		a *= a;
		a %= MOD;
		b /= 2;
	}
	return ans;
}
long long modinv(long long a){
	return modpow(a, MOD - 2);
}
vector<long long> mf = {1};
vector<long long> mfi = {1};
long long modfact(int n){
	if (mf.size() > n){
		return mf[n];
	} else {
		for (int i = mf.size(); i <= n; i++){
			long long next = mf.back() * i % MOD;
			mf.push_back(next);
			mfi.push_back(modinv(next));
		}
		return mf[n];
	}
}
long long modfactinv(int n){
	if (mfi.size() > n){
		return mfi[n];
	} else {
		return modinv(modfact(n));
	}
}
long long modbinom(int n, int k){
	if (n < 0 || k < 0 || k > n){
		return 0;
	} else {
		return modfact(n) * modfactinv(k) % MOD * modfactinv(n - k) % MOD;
	}
}
vector<vector<long long>> matmul(vector<vector<long long>> A, vector<vector<long long>> B){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		for (int j = 0; j < N; j++){
			for (int k = 0; k < N; k++){
				ans[i][k] += A[i][j] * B[j][k];
				ans[i][k] %= MOD;
			}
		}
	}
	return ans;
}
vector<vector<long long>> matexp(vector<vector<long long>> A, long long b){
	int N = A.size();
	vector<vector<long long>> ans(N, vector<long long>(N, 0));
	for (int i = 0; i < N; i++){
		ans[i][i] = 1;
	}
	while (b > 0){
		if (b % 2 == 1){
			ans = matmul(ans, A);
		}
		A = matmul(A, A);
		b /= 2;
	}
	return ans;
}
int main(){
  string S;
  cin >> S;
  int K;
  cin >> K;
  int N = S.size();
  //dp[何文字見た][開き回数][何回変更]
  vector<vector<vector<long long>>> dp(N + 1, vector<vector<long long>>(N + 1, vector<long long>(N + 1, 0)));
  dp[0][0][0] = 1;
  for (int i = 0; i < N; i++){
    for (int j = 0; j <= i; j++){
      for (int k = 0; k <= i; k++){
        if (dp[i][j][k] > 0){
          int open = j, close = i - j;
          int d = open - close;
          //'('
          if (S[i] == '('){
            dp[i + 1][j + 1][k] += dp[i][j][k];
            dp[i + 1][j + 1][k] %= MOD;
          } else {
            dp[i + 1][j + 1][k + 1] += dp[i][j][k];
            dp[i + 1][j + 1][k + 1] %= MOD;
          }
          //')'
          if (d > 0){
            if (S[i] == ')'){
              dp[i + 1][j][k] += dp[i][j][k];
              dp[i + 1][j][k] %= MOD;
            } else {
              dp[i + 1][j][k + 1] += dp[i][j][k];
              dp[i + 1][j][k + 1] %= MOD;
            }
          }
        }
      }
    }
  }
  //S と異なる文字数 (偶数)
  vector<vector<long long>> A(N + 1, vector<long long>(N + 1, 0));
  for (int i = 0; i <= N; i += 2){
    int S = N * (N - 1) / 2;
    if (i >= 2){
      A[i][i - 2] = (i / 2) * (i / 2);
      S -= A[i][i - 2];
    }
    if (i <= N - 2){
      A[i][i + 2] = ((N - i) / 2) * ((N - i) / 2);
      S -= A[i][i + 2];
    }
    A[i][i] = S;
  }
  A = matexp(A, K);
  long long ans = 0;
  for (int i = 0; i <= N; i++){
    ans += dp[N][N / 2][i] * modinv(modpow(modbinom(N / 2, i / 2), 2)) % MOD * A[0][i] % MOD;
  }
  ans %= MOD;
  cout << ans << endl;
}