#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using u64 = uint_fast64_t;
using pii =  pair<int, int>;
using pll =  pair<long long, long long>;
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define all(x) (x).begin(),(x).end()
constexpr char ln =  '\n';
//constexpr long long MOD = 1000000007;
constexpr long long MOD = 998244353;
template<class T1, class T2> inline bool chmax(T1 &a, T2 b) { if (a < b) { a = b; return true;} return false; }
template<class T1, class T2> inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return true;} return false; }
inline int popcount(int x) {return __builtin_popcount(x);}
inline int popcount(long long x) {return __builtin_popcountll(x);}
void print() { cout << "\n"; }
template<class T, class... Args>
void print(const T &x, const Args &... args) {
    cout << x << " ";
    print(args...);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////

template <uint_fast64_t Modulus> 
struct ModInt {
    using u64 = uint_fast64_t;

    u64 a;

    constexpr ModInt(const long long x = 0) noexcept : a(x >= 0 ? x % Modulus : (Modulus - (-x) % Modulus) % Modulus) {}
    constexpr u64 &value() noexcept {return a;}
    constexpr const u64 &value() const noexcept {return a;}
    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 long long rhs) const noexcept {return ModInt(*this) ^= rhs;}
    constexpr bool operator==(const ModInt &rhs) const noexcept {return a == rhs.a;}
    constexpr bool operator!=(const ModInt &rhs) const noexcept {return a != rhs.a;}
    constexpr ModInt &operator+=(const ModInt rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr ModInt &operator/=(ModInt rhs) noexcept {
        u64 exp = Modulus - 2;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }
    constexpr ModInt &operator^=(long long exp) noexcept {
        ModInt rhs = a;
        a = 1;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }

    friend ostream &operator<<(ostream& os, const ModInt& rhs) noexcept {return os << rhs.a;}
    friend istream &operator>>(istream& is, ModInt& rhs) noexcept {long long a; is >> a; rhs = a; return is;}
};

using mint = ModInt<MOD>;

mint dp[310][310][310];
bool check[310][310][310];
int cnt[310];
int rui[310];
int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    string S; cin >> S;
    int N = S.size();
    int K; cin >> K;

    int c = 0;
    rep(i,N) {
        if (S[i]=='0') c++;
        else cnt[c]++;
    }
    //rep(i,4) cout << cnt[i] << endl;
    for (int i = 305; i >= 0; i--) {
        rui[i] = rui[i+1] + cnt[i];
        //cout << rui[i] << endl;
    }
    //y増やした z減らした
    auto dfs=[&](auto&& self, int x, int y, int z)->mint {
        if (check[x][y][z]) return dp[x][y][z];
        //cout << x << " " <<  y << " " << z << endl;
        check[x][y][z] = 1;
        if (y-z==rui[x]) return dp[x][y][z] = 1;
        for (int i = max({cnt[x]-y+z,0}); i <= min({cnt[x]+K-y,rui[x],cnt[x]-(y-z-rui[x+1])}); i++) {
            if (i <= cnt[x]) dp[x][y][z] += self(self,x+1,y,z+cnt[x]-i);
            else dp[x][y][z] += self(self,x+1,y+i-cnt[x],z);
        }
        return dp[x][y][z];
    };

    cout << dfs(dfs,0,0,0) << ln;
}


Measured memory_bytes: 64576