#include <bits/stdc++.h>

using namespace std;

using ll = long long;

constexpr char newl = '\n';
constexpr int MAXS = 300;

// https://noshi91.hatenablog.com/entry/2019/03/31/174006
template <std::uint_fast64_t Modulus>
struct ModInt {
    using u64 = std::uint_fast64_t;

    static constexpr u64 MOD = Modulus;

    u64 val;

    constexpr ModInt(const u64 x = 0) noexcept : val(x % MOD) {}

    constexpr ModInt operator+() const noexcept { return ModInt(*this); }
    constexpr ModInt operator-() const noexcept {
        ModInt res(*this);
        if (res.val != 0) res.val = MOD - res.val;
        return res;
    }

    constexpr bool operator==(const ModInt& rhs) const noexcept { return val == rhs.val; }
    constexpr bool operator!=(const ModInt& rhs) const noexcept { return val != rhs.val; }

    // prefix increment/decrement
    constexpr ModInt& operator++() noexcept { return *this += ModInt(1); }
    constexpr ModInt& operator--() noexcept { return *this -= ModInt(1); }

    // postfix increment/decrement
    constexpr ModInt operator++(int) noexcept {
        ModInt tmp(*this);
        ++*this;
        return tmp;
    }
    constexpr ModInt operator--(int) noexcept {
        ModInt tmp(*this);
        --*this;
        return tmp;
    }

    constexpr ModInt operator+(const ModInt& rhs) const noexcept {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt& rhs) const noexcept {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt& rhs) const noexcept {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt& rhs) const noexcept {
        return ModInt(*this) /= rhs;
    }

    constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
        val += rhs.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
        if (val < rhs.val) val += MOD;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
        val = val * rhs.val % MOD;
        return *this;
    }

    // prime Modulus only
    constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    // prime Modulus only
    constexpr ModInt inv() const noexcept {
        return pow(*this, MOD - 2);
    }
};

template<std::uint_fast64_t Modulus>
constexpr ModInt<Modulus> pow(ModInt<Modulus> x, std::uint_fast64_t n) {
    ModInt<Modulus> res(1);
    while (n) {
        if (n & 1) res *= x;
        x *= x;
        n >>= 1;
    }
    return res;
}

template<std::uint_fast64_t Modulus>
istream& operator>>(istream& is, ModInt<Modulus>& x) {
    std::uint_fast64_t val;
    is >> val;
    x = ModInt<Modulus>(val);
    return is;
}

template<std::uint_fast64_t Modulus>
ostream& operator<<(ostream& os, const ModInt<Modulus>& x) {
    return os << x.val;
}

using mint = ModInt<998244353>;

// 000 1 00 1 1  1

// dp[index][操作回数][未決定の0の個数]

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    string s;
    int K;
    cin >> s >> K;
    reverse(s.begin(), s.end());

    int n = s.size();
    K = min(K, MAXS);

    vector<int> v;
    int cnt0 = 0;
    {
        int tmp = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] == '0') {
                v.push_back(tmp);
                tmp = 0;
            } else {
                ++tmp;
                ++cnt0;
            }
        }
        v.push_back(0);
    }
    int sz = v.size();

    // vector< vector< vector<mint> > > dp(sz + 1, vector< vector<mint> >(K + 1, vector<mint>(cnt0 + 1, 0)));
    // dp[sz][0][cnt0] = 1;

    vector< vector<mint> > dp(K + 1, vector<mint>(cnt0 + 1, 0));
    dp[0][0] = 1;

    int sum = 0;
    for (int i = 0; i < sz; ++i) {
        vector< vector< vector<mint> > > dp2(K + 1, vector< vector<mint> >(sum + 1, vector<mint>(v[i] + 1, 0)));
        for (int j = 0; j <= K; j++) {
            for (int k = sum; k >= 0; k--) {
                dp2[j][k][v[i]] = dp[j][k];
            }
        }
        
        dp.assign(K + 1, vector<mint>(cnt0 + 1, 0));
        for (int j = 0; j <= K; j++) {
            for (int k = sum; k >= 0; k--) {
                for (int l = v[i]; l >= 0; l--) {
                    if (l < v[i]) dp2[j][k][l] += dp2[j][k][l + 1];
                    if (l == 0 && j > 0 && k < sum) dp2[j][k][l] += dp2[j - 1][k + 1][l];
                    dp[j][k + l] += dp2[j][k][l];
                }
            }
        }

        sum += v[i];
    }

    mint ans = 0;
    for (int i = 0; i <= K; i++) {
        ans += dp[i][0];
    }
    cout << ans << newl;

    return 0;
}

Measured memory_bytes: 21508