#include <bits/stdc++.h>
#define int long long
#define ll long long
using ull = unsigned long long;
using namespace std;
#define dump(x)                             \
    if (dbg) {                              \
        cerr << #x << " = " << (x) << endl; \
    }
#define overload4(_1, _2, _3, _4, name, ...) name
#define FOR1(n) for (ll i = 0; i < (n); ++i)
#define FOR2(i, n) for (ll i = 0; i < (n); ++i)
#define FOR3(i, a, b) for (ll i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FORR(i, a, b) for (int i = (a); i <= (b); ++i)
#define bit(n, k) ((n >> k) & 1) /*nのk bit目*/
namespace mydef {
const int INF = 1ll << 60;
const int MOD = 998244353;
template <class T>
bool chmin(T& a, const T& b) {
    if (a > b) {
        a = b;
        return 1;
    } else
        return 0;
}
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return 1;
    } else
        return 0;
}
void Yes(bool flag = true) {
    if (flag)
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
}
void No(bool flag = true) {
    Yes(!flag);
}
void YES(bool flag = true) {
    if (flag)
        cout << "YES" << endl;
    else
        cout << "NO" << endl;
}
void NO(bool flag = true) {
    YES(!flag);
}
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T& val) {
    std::fill((T*)array, (T*)(array + N), val);
}
bool dbg = false;
}  // namespace mydef
using namespace mydef;
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(), (v).end()
#define SZ(x) ((int)(x).size())
#define vi vector<int>
#define vvi vector<vector<int>>
#define vp vector<pair<int, int>>
#define vvp vector<vector<pair<int, int>>>
#define pi pair<int, int>
//#define P pair<int, int>
//#define V vector<int>
//#define S set<int>
#define asn ans
template <uint MD>
struct ModInt {
    using M = ModInt;
    const static M G;
    uint v;
    ModInt(ll _v = 0) { set_v(_v % MD + MD); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(ull(v) * r.v % MD); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    M pow(ll n) const {
        M x = *this, r = 1;
        while (n) {
            if (n & 1)
                r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    M inv() const { return pow(MD - 2); }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
    friend istream& operator>>(istream& is, M& r) { return is >> r.v; }
};
using Mint = ModInt<MOD>;
const int MN = 1000000;
Mint fact[MN], iFac[MN];
void first() {
    fact[0] = Mint(1);
    for (int i = 1; i < MN; i++)
        fact[i] = fact[i - 1] * Mint(i);
    iFac[MN - 1] = fact[MN - 1].inv();
    for (int i = MN - 1; i >= 1; i--) {
        iFac[i - 1] = iFac[i] * Mint(i);
    }
    assert(fact[2345] * iFac[2345] == Mint(1));
}
Mint C(int n, int k) {
    if (n < k || k < 0)
        return Mint(0);
    return fact[n] * iFac[k] * iFac[n - k];
}

string S;
vi s;
int K;
int mp[333];

Mint dp[333][333][333];

void solve() {
    while (S.size() > 0 && S[0] == 1)
        S.erase(S.begin());
    if (S.size() == 0) {
        cout << 1 << endl;
        return;
    }
    int cnt1 = 0;
    for (auto& c : S)
        cnt1 += c;
    chmin(K, cnt1);

    /*
    int tmp = 0;
    for (int i = 0; i < S.size(); i++) {
        if(S[i] == 1){
        }
    }
    */

    s.emplace_back(0);
    {
        int pre = 0;
        for (auto& c : S) {
            if ((int)c == pre) {
                (s.back())++;
            } else {
                pre = !pre;
                s.emplace_back(1);
            }
        }
    }

    int max_0 = 0;

    int now = 0;
    dp[0][0][1] = 1;
    for (int i = 0; i < s.size(); i++) {
        int n = s[i];
        if (now == 1) {
            for (int a = 0; a <= K; a++) {
                for (int m = 0; m <= n; m++) {
                    for (int c = max_0; c >= 0; c--) {
                        //a:既に動かした1の個数
                        //m:動かす1の個数
                        //c:行き先の0の個数
                        for (int d = 1; d <= c; d++) {
                            if (m > 0)
                                dp[a + m][i + 1][d] += dp[a][i][c] * C((c - d) + m - 1, m - 1);
                        }
                        if (m == 0)
                            dp[a][i + 1][c] += dp[a][i][c];

                        //a:既に動かした1の個数
                        //m:動かす1の個数
                        //c:行き先の0の個数
                        //dp[a + m][i + 1][c] += dp[a][i][c] * C(c + m - 1, m);
                    }
                }
            }
        } else {
            max_0 += n;
            //0の場合
            for (int a = 0; a <= 300; a++) {
                //a:既に動かした1の個数
                for (int c = 0; c <= 300; c++) {
                    //c:行き先の0の個数
                    dp[a][i + 1][c + (n - 1)] += dp[a][i][c];
                    if (i - 1 >= 1) {
                        dp[a][i + 1][c + (n - 1)] -= dp[a][i - 1][c];
                        dp[a][i + 1][c + n] += dp[a][i - 1][c];
                    }
                }
            }
        }
        now ^= 1;
    }


    /*
    for (int j = 0; j < 10; j++) {
        for (int i = 0; i < 10; i++) {
            for (int k = 0; k < 10; k++) {
                cerr << dp[i][j][k] << " ";
            }
            cerr << endl;
        }
        cerr << endl;
    }
    */

    Mint ans = 0;
    for (int i = 0; i <= K; i++) {
        for (int j = 0; j <= 300; j++) {
            ans += dp[i][s.size()][j];
        }
    }

    cout << ans << endl;
}

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

    cin >> S >> K;
    for (auto& c : S)
        c -= '0';

    solve();
    return 0;
}


Measured memory_bytes: 155724