#include <bits/stdc++.h>
using namespace std;
const long long MOD=998244353;

template<uint_fast64_t Modulus> class modint{
    using u64=uint_fast64_t;
    public:
    u64 a;
    constexpr modint(const u64 x=0) noexcept:a(((x%Modulus)+Modulus)%Modulus){}
    constexpr u64 &value() noexcept{return a;}
    constexpr const u64 &value() const noexcept{return a;}
    constexpr modint &operator+=(const modint &rhs) noexcept{
        a+=rhs.a;
        if (a>=Modulus) a-=Modulus;
        return *this;
    }
    constexpr modint operator+(const modint &rhs) const noexcept{
        return modint(*this)+=rhs;
    }
    constexpr modint &operator++() noexcept{
        return ++a,*this;
    }
    constexpr modint operator++(int) noexcept{
        modint t=*this; return ++a,t;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{
        if (a<rhs.a) a+=Modulus;
        a-=rhs.a;
        return *this;
    }
    constexpr modint operator-(const modint &rhs) const noexcept{
        return modint(*this)-=rhs;
    }
    constexpr modint &operator--() noexcept{
        return --a,*this;
    }
    constexpr modint operator--(int) noexcept{
        modint t=*this; return --a,t;
    }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        a=a*rhs.a%Modulus;
        return *this;
    }
    constexpr modint operator*(const modint &rhs) const noexcept{
        return modint(*this)*=rhs;
    }
    constexpr modint &operator/=(modint rhs) noexcept{
        u64 exp=Modulus-2;
        while(exp){
            if (exp&1) *this*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return *this;
    }
    constexpr modint operator/(const modint &rhs) const noexcept{
        return modint(*this)/=rhs;
    }
    constexpr modint operator-() const noexcept{
        return modint(Modulus-a);
    }
    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 bool operator!() const noexcept{return !a;}
    friend constexpr modint pow(modint rhs,long long exp) noexcept{
        modint res{1};
        while(exp){
            if (exp&1) res*=rhs;
            rhs*=rhs; exp>>=1;
        }
        return res;
    }
    template<class T> friend constexpr modint operator+(T x,modint y) noexcept{
        return modint(x)+y;
    }
    template<class T> friend constexpr modint operator-(T x,modint y) noexcept{
        return modint(x)-y;
    }
    template<class T> friend constexpr modint operator*(T x,modint y) noexcept{
        return modint(x)*y;
    }
    template<class T> friend constexpr modint operator/(T x,modint y) noexcept{
        return modint(x)/y;
    }
    friend ostream &operator<<(ostream &s,const modint &rhs) noexcept{
        return s << rhs.a;
    }
    friend istream &operator>>(istream &s,modint &rhs) noexcept{
        u64 a; rhs=modint{(s >> a,a)}; return s;
    }
};

using mint=modint<MOD>;

const int MAX_N=310;

mint dp[MAX_N][MAX_N][MAX_N];
mint imos[MAX_N][MAX_N],diag[MAX_N][MAX_N];

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    string S; int K; cin >> S >> K;
    S+='0';
    vector<int> ones;
    for (int i=0;i<S.size();++i){
        int cnt=0;
        while(S[i]=='1') ++i,++cnt;
        ones.emplace_back(cnt);
    }
    int n=ones.size();
    reverse(ones.begin(),ones.end());
    vector<int> sum(n+1,0);
    for (int i=0;i<n;++i) sum[i+1]=sum[i]+ones[i];
    dp[0][0][0]=1;
    for (int i=0;i<n;++i){
        for (int j=0;j<MAX_N;++j){
            for (int k=0;k<MAX_N;++k){
                imos[j][k]=diag[j][k]=0;
            }
        }
        for (int j=0;j<=sum[i];++j){
            for (int k=0;k<=j;++k){
                imos[j][k]+=dp[i][j][k];
                imos[j+ones[i]][k]-=dp[i][j][k];
                diag[j+ones[i]][k]+=dp[i][j][k];
                diag[sum[i+1]+1][k+sum[i+1]-ones[i]+1]-=dp[i][j][k];
            }
        }
        for (int k=0;k<MAX_N;++k){
            for (int j=0;j<MAX_N-1;++j){
                imos[j+1][k]+=imos[j][k];
            }
        }
        for (int j=0;j<MAX_N-1;++j){
            for (int k=0;k<MAX_N-1;++k){
                diag[j+1][k+1]+=diag[j][k];
            }
        }
        for (int j=0;j<MAX_N;++j){
            for (int k=0;k<MAX_N;++k){
                dp[i+1][j][k]+=imos[j][k]+diag[j][k];
            }
        }
    }
    mint ans=0;
    for (int k=0;k<=min(MAX_N-1,K);++k) ans+=dp[n][sum[n]][k];
    cout << ans << '\n';
}

Measured memory_bytes: 230292