#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
using mint = modint998244353;
const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define endl "\n"
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
	vector<mint> fact, ifact;
	combination(int n) :fact(n + 1), ifact(n + 1) {
		assert(n < mod);
		fact[0] = 1;
		for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
		ifact[n] = fact[n].inv();
		for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
	}
	mint operator()(int n, int k) { return com(n, k); }
	mint com(int n, int k) {
		//負の二項係数を考慮する場合にコメントアウトを外す
		//if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[k] * ifact[n - k];
	}
	mint inv(int n, int k) {
		//if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return ifact[n] * fact[k] * fact[n - k];
	}
	mint p(int n, int k) { return fact[n] * ifact[n - k]; }
}c(200005);
vector<vector<mint>> mul(vector<vector<mint>>&A, vector<vector<mint>>&B) {
	vector<vector<mint>> C(A.size(), vector<mint>(B[0].size()));
	rep(i, A.size()) rep(j, B[0].size()) rep(k, A[0].size()) C[i][j] += A[i][k] * B[k][j];
	//rep(i, A.size()) rep(j, B[0].size()) rep(k, A[0].size()) C[i][j] += A[i][k] & B[k][j];
	return C;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	string s; cin >> s;
	int k; cin >> k;
	int sz = s.size() / 2;
	vector<vector<mint>> mans(sz + 1, vector<mint>(sz + 1));
	vector<vector<mint>> mpow(sz + 1, vector<mint>(sz + 1));
	mans[0][0] = 1;
	rep(i, sz + 1) {
		mpow[i][i] = sz * (2 * sz - 1) - i * i - (sz - i)*(sz - i);
		if (0 < i) {
			mpow[i - 1][i] = i * i;
		}
		if (i < sz) {
			mpow[i + 1][i] = (sz - i)*(sz - i);
		}
	}
	int copyk = k;
	while (copyk > 0) {
		if (1 == copyk % 2) mans = mul(mpow, mans);
		copyk /= 2;
		mpow = mul(mpow, mpow);
	}
	vector<vector<vector<mint>>> dp(2 * sz + 1, vector<vector<mint>>(2 * sz + 5, vector<mint>(sz + 5)));
	dp[0][0][0] = 1;
	for (int i = 0; i < 2 * sz; ++i) {
		for (int j = 0; j <= 2 * sz; ++j) {
			for (int k = 0; k <= sz; ++k) {
				if (s[i] == '(') {
					dp[i + 1][j + 1][k] += dp[i][j][k];
					if (0 < j) {
						dp[i + 1][j - 1][k + 1] += dp[i][j][k];
					}
				}
				else {
					dp[i + 1][j + 1][k] += dp[i][j][k];
					if (0 < j) {
						dp[i + 1][j - 1][k] += dp[i][j][k];
					}
				}
			}
		}
	}
	mint ans = 0;
	rep(i, sz + 1) {
		ans += dp[2 * sz][0][i] * mans[i][0] / (c(sz, i) *c(sz, i));
	}
	cout << ans.val() << endl;
	return 0;
}