#include <bits/stdc++.h>
using namespace std;
using lint         = long long;
constexpr lint inf = 1LL << 60;
constexpr lint mod = 998244353;

template <int mod>
struct modint {
    lint v;
    modint() : v(0) {}
    modint(signed v) : v(v) {}
    modint(lint t) {
        v = t % mod;
        if (v < 0)
            v += mod;
    }

    modint pow(lint k) {
        modint res(1), tmp(v);
        while (k) {
            if (k & 1)
                res *= tmp;
            tmp *= tmp;
            k >>= 1;
        }
        return res;
    }
    static modint add_identity() { return modint(0); }
    static modint mul_identity() { return modint(1); }
    modint inv() { return pow(mod - 2); }

    modint &operator+=(modint a) {
        v += a.v;
        if (v >= mod)
            v -= mod;
        return *this;
    }
    modint &operator-=(modint a) {
        v += mod - a.v;
        if (v >= mod)
            v -= mod;
        return *this;
    }
    modint &operator*=(modint a) {
        v = v * a.v % mod;
        return *this;
    }
    modint &operator/=(modint a) { return (*this) *= a.inv(); }

    modint operator+(modint a) const { return modint(v) += a; };
    modint operator-(modint a) const { return modint(v) -= a; };
    modint operator*(modint a) const { return modint(v) *= a; };
    modint operator/(modint a) const { return modint(v) /= a; };

    modint operator-() const { return v ? modint(mod - v) : modint(v); }

    bool operator==(const modint a) const { return v == a.v; }
    bool operator!=(const modint a) const { return v != a.v; }
    bool operator<(const modint a) const { return v < a.v; }
};
using mint = modint<mod>;
ostream &operator<<(ostream &os, mint m) { return os << m.v; }

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    string s;
    cin >> s;
    int ns = s.size();
    lint k;
    cin >> k;
    vector<int> ones;
    int one = 0;
    for (int i = 0; i < ns; ++i) {
        if (s[i] == '0') {
            ones.push_back(one);
            one = 0;
        } else {
            one++;
        }
    }
    ones.push_back(one);
    int m = ones.size();
    vector<vector<vector<lint>>> dp(m + 1, vector<vector<lint>>(ns + 1, vector<lint>(ns + 1, 0)));
    for (int i = 0; i <= m; ++i) {
        for (int j = 0; j <= ns; ++j) {
            for (int l = 0; l <= ns; ++l) {
                dp[i][j][l] = 0;
            }
        }
    }
    dp[0][0][0] = 1;
    for (int i = 1; i <= m - 1; ++i) {
        vector<vector<lint>> temp(400, vector<lint>(400, 0));
        for (int j = 0; j <= ns; ++j) {
            for (int l = 0; l <= ns; ++l) {
                temp[j][l]  = dp[i - 1][j][l];
                dp[i][j][l] = dp[i - 1][j][l];
            }
        }
        for (int j = 0; j <= ns; ++j) {
            for (int l = 0; l <= ns; ++l) {
                for (int x = 1; x <= ones[i - 1]; ++x) { // total  < 300
                    if (k - x < 0 || l - x < 0)
                        break;
                    temp[j][l - x] += temp[j][l];
                    temp[j][l - x] %= mod;
                }
            }
        }
        for (int j = 0; j <= ns; ++j) {
            for (int l = 0; l <= ns; ++l) {
                temp[j][l] -= dp[i - 1][j][l];
                if (temp[j][l] < 0)
                    temp[j][l] += mod;
            }
        }

        for (int j = 1; j <= ns; ++j) {
            for (int l = 1; l <= ns; ++l) {
                if (j + l >= ns)
                    break;
                dp[i][j + l - 1][l] += dp[i][j + l - 2][l - 1];
                dp[i][j + l - 1][l] %= mod;
            }
        }
        for (int j = 2; j <= ns; ++j) {
            for (int l = 1; l <= ns; ++l) {
                if (j + l >= ns)
                    break;
                dp[i][l][j + l - 1] += dp[i][l - 1][j + l - 2];
                dp[i][l][j + l - 1] %= mod;
            }
        }

        for (int j = 0; j <= ns; ++j) {
            for (int l = 0; l <= ns; ++l) {
                dp[i][j][l] += temp[j][l];
                dp[i][j][l] %= mod;
            }
        }
    }
    int id   = min(k, lint(ns));
    lint ret = 0;
    for (int i = 0; i <= id; ++i) {
        for (int j = 0; j <= ones[m - 1]; ++j) {
            ret += dp[m - 1][i][j];
            ret %= mod;
        }
    }
    cout << ret << endl;
    return 0;
}

Measured memory_bytes: 219588