#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
#define FOR(i,a,b) for (int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(x) (x).begin(),(x).end()
// const long long MOD=1e9+7;
const long long MOD=998244353;
const int INF=1e9;
const long long IINF=1e18;
const int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
const char dir[4]={'D','R','U','L'};
#define LOCAL

template<typename T>
istream &operator>>(istream &is,vector<T> &v){
    for (T &x:v) is >> x;
    return is;
}
template<typename T>
ostream &operator<<(ostream &os,const vector<T> &v){
    for (int i=0;i<v.size();++i){
        os << v[i] << (i+1==v.size()?"": " ");
    }
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p){
    cout << '(' << p.first << ',' << p.second << ')';
    return os;
}
template<typename T,typename U>
ostream &operator<<(ostream &os,const map<T,U> &m){
    os << '{';
    for (auto itr=m.begin();itr!=m.end();++itr){
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr!=m.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}
template<typename T>
ostream &operator<<(ostream &os,const set<T> &s){
    os << '{';
    for (auto itr=s.begin();itr!=s.end();++itr){
        os << *itr;
        if (++itr!=s.end()) os << ',';
        --itr;
    }
    os << '}';
    return os;
}

void debug_out(){cerr << '\n';}
template<class Head,class... Tail>
void debug_out(Head&& head,Tail&&... tail){
    cerr << head;
    if (sizeof...(Tail)>0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) cerr << " ";\
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n';\
cerr << " ";\
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<typename T> T gcd(T x,T y){return y!=0?gcd(y,x%y):x;}
template<typename T> T lcm(T x,T y){return x/gcd(x,y)*y;}

template<class T1,class T2> inline bool chmin(T1 &a,T2 b){
    if (a>b){a=b; return true;} return false;
}
template<class T1,class T2> inline bool chmax(T1 &a,T2 b){
    if (a<b){a=b; return true;} return false;
}
#pragma endregion

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=5e5+10;
vector<mint> fac(MAX),finv(MAX),inv(MAX);
void COMinit(){
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for (int i=2;i<MAX;++i){
        fac[i]=fac[i-1]*i;
        inv[i]=-inv[MOD%i]*(MOD/i);
        finv[i]=finv[i-1]*inv[i];
    }
}
mint COM(int n,int k){
    if (n<k||n<0||k<0) return 0;
    return fac[n]*finv[k]*finv[n-k];
}

// Be careful with the value of MAX and conducting COMinit()

const int MAX_N=610;

mint dp[MAX_N][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(ALL(ones));
    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){
        vector<vector<mint>> imos(MAX_N,vector<mint>(MAX_N,0))
                            ,diag(MAX_N,vector<mint>(MAX_N,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;++j){
            for (int k=0;k<MAX_N;++k){
                if (j-1>=0&&k-1>=0) diag[j][k]+=diag[j-1][k-1];
            }
        }
        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];
            }
        }
        /*
        for (int j=0;j<=sum[i+1];++j)
            for (int k=0;k<=sum[i+1];++k)
                cerr << imos[j][k] << (k+1==sum[i+1]+1?'\n':' ');
        cerr << '\n';
        for (int j=0;j<=sum[i+1];++j)
            for (int k=0;k<=sum[i+1];++k)
                cerr << dp[i+1][j][k] << (k+1==sum[i+1]+1?'\n':' ');
        cerr << '#' << i+1 << '\n';
        */
    }
    /*
    cerr << ones << '\n';
    cerr << sum << '\n';
    */
    mint ans=0;
    for (int k=0;k<=min(MAX_N-1,K);++k) ans+=dp[n][sum[n]][k];
    cout << ans << '\n';




    /*
    vector<int> suf(n+1,0);
    for (int i=n-1;i>=0;--i) suf[i]=suf[i+1]+ones[i];
    dp[0][0][0]=1;
    for (int i=0;i<n;++i){
        vector<vector<mint>> imos(MAX_N,vector<mint>(MAX_N,0))
                            ,diag(MAX_N,vector<mint>(MAX_N,0));
        for (int j=0;j<=sum;++j){
            for (int k=0;k<MAX_N;++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[j+suf[i]+1][k+suf[i]-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;++j){
            for (int k=0;k<MAX_N;++k){
                if (j-1>=0&&k-1>=0) diag[j][k]+=diag[j-1][k-1];
            }
        }
        for (int j=0;j<=sum;++j)
            for (int k=0;k<=sum;++k)
                cerr << imos[j][k] << (k+1==sum+1?'\n':' ');
        cerr << '\n';
        for (int j=0;j<=sum;++j)
            for (int k=0;k<=sum;++k)
                cerr << diag[j][k] << (k+1==sum+1?'\n':' ');
        cerr << '\n';
        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];
            }
        }
        for (int j=0;j<=sum;++j)
            for (int k=0;k<=sum;++k)
                cerr << dp[i+1][j][k] << (k+1==sum+1?'\n':' ');
        cerr << '#' << i+1 << '\n';
    }
    mint ans=0;
    for (int k=0;k<=min(MAX_N-1,K);++k) ans+=dp[n][sum][k];
    cout << ans << '\n';
    cerr << ones << '\n';
    cerr << suf << '\n';
    */
}

Measured memory_bytes: 892808