#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define LINF (9223372036854775807LL)
#define EPS (1e-10)
#define endl ('\n')
//#define MOD 1000000007LL
#define MOD 998244353LL
//#define MOD 18446744069414584321ULL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,n) for(lint i=0;i<lint(n);++i)
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrep(i,n) for(lint i=lint(n)-1;i>=0;--i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}

class mint {
  using u64 = std::uint_fast64_t;
    public:
    u64 a;
    constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
    constexpr u64 &value()noexcept{return a;}
    constexpr const u64 &value() const noexcept {return a;}
    constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
    constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
    constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
    constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
    constexpr mint &operator+=(const mint rhs) noexcept {
        a += rhs.a;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint &operator-=(const mint rhs) noexcept {
        if (a<rhs.a)a += get_mod();
        a -= rhs.a;
        return *this;
    }
    constexpr mint &operator*=(const mint rhs) noexcept {
        a = a * rhs.a % get_mod();
        return *this;
    }
    constexpr mint operator++(int n) noexcept {
        a += 1;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint operator--(int n) noexcept {
        if (a<1)a += get_mod();
        a -= 1;
        return *this;
    }
    constexpr mint &operator/=(mint rhs) noexcept {
        u64 exp=get_mod()-2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    constexpr bool operator==(mint x) noexcept {
        return a==x.a;
    }
    constexpr bool operator!=(mint x) noexcept {
        return a!=x.a;
    }
	constexpr bool operator<(mint x) noexcept {
        return a<x.a;
    }
	constexpr bool operator>(mint x) noexcept {
        return a>x.a;
    }
	constexpr bool operator<=(mint x) noexcept {
        return a<=x.a;
    }
	constexpr bool operator>=(mint x) noexcept {
        return a>=x.a;
    }
    constexpr static int root(){
        mint root = 2;
        while(root.pow((get_mod()-1)>>1).a==1)root++;
        return root.a;
    }
    constexpr mint pow(long long n){
        long long x=a;
        mint ret = 1;
        while(n>0) {
            if(n&1)(ret*=x);
            (x*=x)%=get_mod();
            n>>=1;
        }
        return ret;
    }
    constexpr mint inv(){
        return pow(get_mod()-2);
    }
    static vector<mint> fac,ifac;
    static bool init;
    constexpr static int mx=10000001;
    void build(){
        init=0;
        fac.resize(mx);
        ifac.resize(mx);
        fac[0]=1,ifac[0]=1;
        for(int i=1;i<mx;i++)fac[i]=fac[i-1]*i;
        ifac[mx-1]=fac[mx-1].inv();
        for(int i=mx-2;i>=0;i--)ifac[i]=ifac[i+1]*(i+1);
    }
    mint comb(lint b){
        if(init)build();
        if(a==0&&b==0)return 1;
        if((lint)a<b||a<0)return 0;
        return fac[a]*ifac[a-b]*ifac[b];
    }
    mint fact(){
        if(init)build();
        return fac[a];
    }
    mint fact_inv(){
        if(init)build();
        return ifac[a];
    }
    friend ostream& operator<<(ostream& lhs, const mint& rhs) noexcept {
        lhs << rhs.a;
        return lhs;
    }
    friend istream& operator>>(istream& lhs,mint& rhs) noexcept {
        lhs >> rhs.a;
        return lhs;
    }
    constexpr static u64 get_mod(){return MOD;}
};
vector<mint> mint::fac;
vector<mint> mint::ifac;
bool mint::init=1;

int main(){
    string s;
    lint k;
    cin>>s>>k;
    if(count(all(s),'0')==0){
        cout<<1<<endl;
        return 0;
    }
    if(count(all(s),'1')==0){
        cout<<1<<endl;
        return 0;
    }
    vec v(1,0);
    rep(i,s.size()){
        if(s[i]=='0')v.push_back(0);
        else v.back()++;
    }
    reverse(all(v));
    lint m=v.size();
    vector<lint>v2(m+1,0);
    rep(i,m)v2[i+1]+=v2[i]+v[i];
    auto dp=make_vector<mint>(0,m+1,v2.back()+1,2*v2.back()+1);
    dp[0][0][0]=1;
    repi(i,1,m+1){
        rep(j,v2[i-1]+1)repi(k,j,v2[i]+1)rep(l,2*v2.back()+1){
            if(l+abs(v[i-1]-(k-j))<=2*v2.back()){
                dp[i][k][l+abs(v[i-1]-(k-j))]+=dp[i-1][j][l];
            }
        }
    }
    mint ans=0;
    rep(j,min(k*2,2*v2.back())+1){
        ans+=dp[m][v2.back()][j];
    }
    cout<<ans<<endl;
}

Measured memory_bytes: 66976