#include <bits/stdc++.h>

using namespace std;

#define REP(i, n) for (int i=0; i<(n); ++i)
#define RREP(i, n) for (int i=(int)(n)-1; i>=0; --i)
#define FOR(i, a, n) for (int i=(a); i<(n); ++i)
#define RFOR(i, a, n) for (int i=(int)(n)-1; i>=(a); --i)

#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()

#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl
#define DEBUG(x) cerr<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl;

template<class T>
ostream &operator<<(ostream &os, const vector <T> &v) {
    os << "[";
    REP(i, SZ(v)) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "]";
}

template<class T, class U>
ostream &operator<<(ostream &os, const pair <T, U> &p) {
    return os << "(" << p.first << " " << p.second << ")";
}

template<class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
//using vi = vector<int>;
//using vll = vector<ll>;
//using vvi = vector<vi>;
//using vvll = vector<vll>;

const ll MOD = 1e9 + 7;
const int INF = INT_MAX / 2;
const ll LINF = LLONG_MAX / 2;
const ld eps = 1e-9;

int gcd(int a, int b) {
    if (a == 0) return b;
    return gcd(b % a, a);
}

template<int64_t mod>
class modint {
    int64_t x;

public:
    modint(int64_t x = 0) : x(x < 0 ? ((x % mod) + mod) % mod : x % mod) {}

    const modint operator-() const { return x == 0 ? 0 : mod - x; }

    modint& operator+=(const modint& rhs) {
        if ((x += rhs.x) >= mod) x -= mod;
        return *this;
    }
    modint& operator-=(const modint& rhs) {
        return *this += -rhs;
    }
    modint& operator*=(const modint& rhs) {
        (x *= rhs.x) %= mod;
        return *this;
    }
    modint& operator/=(const modint& rhs) {
        return *this *= rhs.pow(mod - 2);
    }

    friend const modint operator+(modint lhs, const modint& rhs) {
        return lhs += rhs;
    }
    friend const modint operator-(modint lhs, const modint& rhs) {
        return lhs -= rhs;
    }
    friend const modint operator*(modint lhs, const modint& rhs) {
        return lhs *= rhs;
    }
    friend const modint operator/(modint lhs, const modint& rhs) {
        return lhs /= rhs;
    }

    const modint pow(int64_t n) const {
        modint ret = 1, tmp = *this;
        while (n) {
            if (n & 1) ret *= tmp;
            tmp *= tmp; n >>= 1;
        }
        return ret;
    }

    friend bool operator==(const modint& lhs, const modint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const modint& lhs, const modint& rhs) {
        return lhs.x != rhs.x;
    }

    friend ostream& operator<<(ostream& os, const modint& a) {
        return os << a.x;
    }
    friend istream& operator>>(istream& is, modint& a) {
        int64_t tmp; is >> tmp; a = tmp;
        return is;
    }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);

    // ifstream in("in.txt");
    // cin.rdbuf(in.rdbuf());

    string S; cin >> S;
    int K; cin >> K;

    using Int = modint<998244353>;

    vector<int> A;
    {
        int cnt = 0;
        for (char c : S) {
            if (c == '0') ++cnt;
            else if (cnt > 0) A.push_back(cnt);
        }
    }

    if (A.empty()) {
        cout << 1 << endl;
        return 0;
    }

    sort(ALL(A));

    int s = A.size();
    unordered_map<int,int> cntA;
    for (int a : A) ++cntA[a];

    int maxA = *max_element(ALL(A));
    int maxCnt = 0;
    for (auto& tp : cntA) chmax(maxCnt, tp.second);


    using vi = vector<Int>;
    using vvi = vector<vi>;
    using vvvi = vector<vvi>;
    using vvvvi = vector<vvvi>;

    //vvvvi dp(s+1, vvvi(s+1, vvi(maxA+1, vi(maxCnt+1))));
    vvvvi dp(s+1, vvvi(1, vvi(1, vi(1))));

    dp[0][0][0][0] = 1;
    for (int i = 0; i < s; ++i) {
        dp[i + 1].resize(i + 2);

        for (int j = 0; j <= i + 1; ++j) {
            dp[i + 1][j].resize(A[i] + 1);

            for (int a = 0; a <= A[i]; ++a) {
                dp[i + 1][j][a].resize(cntA[a] + 1);
            }
        }
    }

    for (int i = 0; i < s; ++i) {

        for (int j = 0; j <= i; ++j) {

            for (int a = 0; a <= A[i]; ++a) {

                for (int b = 0; b <= min(i > 0 ? A[i-1] : 0, a); ++b) {

                    if (b == a) {
                        for (int p = 0; p <= cntA[a]; ++p) {

                            if (p+1 <= cntA[a]) {
                                dp[i+1][j][a][p+1] += dp[i][j][b][p];
                            }
                            else if (j+1 <= i+1) {
                                dp[i+1][j+1][a][p] += dp[i][j][b][p];
                            }

                        }
                    }
                    else {
                        if (cntA[a] > 0) {
                            dp[i+1][j][a][1] += accumulate(ALL(dp[i][j][b]), Int{0});
                        } else if (j+1 <= i+1) {
                            dp[i+1][j+1][a][0] += accumulate(ALL(dp[i][j][b]), Int{0});
                        }
                    }
                }
            }
        }
    }

    Int ans = 0;

    for (int k = 0; k <= min(s, K); ++k) {
        for (int a = 0; a <= maxA; ++a) {
            ans += accumulate(ALL(dp[s][k][a]), Int{0});
        }
    }

    cout << ans << endl;

    return 0;
}


Measured memory_bytes: 131804