#include <bits/stdc++.h>
using namespace std;using ll=long long;using uint=unsigned int;using pii=pair<int,int>;using pll=pair<ll,ll>;using ull = unsigned long long;using ld=long double;template<typename T>void _(const char*s,T h){cerr<<s<<" = "<<h<<"\n";}template<typename T,typename...Ts>void _(const char*s,T h,Ts...t){int b=0;while(((b+=*s=='(')-=*s==')')!=0||*s!=',')cerr<<*s++;cerr<<" = "<<h<<",";_(s+1,t...);}// break continue pop_back 998244353
#define int ll
#define pii pll
#define f first
#define s second
#define pb emplace_back
#define forn(i,n) for(int i=0;i<(n);++i)
#define sz(a)((int)(a).size())
#define sqr(x) ((x)*(x))
struct init{init(){cin.tie(0);iostream::sync_with_stdio(0);cout<<fixed<<setprecision(10);cerr<<fixed<<setprecision(5);}~init(){
#ifdef LOCAL
#define dbg(...) _(#__VA_ARGS__,__VA_ARGS__)
cerr<<"Time elapsed: "<<(double)clock()/CLOCKS_PER_SEC<<"s.\n";
#else
#define dbg(...) 
#endif
}}init;template<typename T,typename U>void upx(T&x,U y){if(x<y)x=y;}template<typename T,typename U>void upn(T&x,U y){if(x>y)x=y;}mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());const int D=4,dx[]={+1,0,-1,0},dy[]={0,+1,0,-1};
const int32_t M=998244353;
int32_t rev(int32_t x,int32_t m){
    if(x==1)return 1;
    return (1-(ll)rev(m%x,x)*m)/x+m;
}
struct mint{
    int32_t x;
    mint():x(0){}
    mint(int32_t xx):x(xx%M){if(x<0)x+=M;}
    mint(ll xx):x(xx%M){if(x<0)x+=M;}
    mint& operator+=(mint b){if((x+=b.x)>=M)x-=M;return *this;}
    mint operator+(mint b){mint res=*this;res+=b;return res;}
    mint& operator-=(mint b){if((x-=b.x)<0)x+=M;return *this;}
    mint operator-(mint b){mint res=*this;res-=b;return res;}
    mint& operator*=(mint b){x=(ll)x*b.x%M;return *this;}
    mint operator*(mint b){mint res=*this;res*=b;return res;}
    mint inverse(){return rev(x,M);}
    mint& operator/=(mint b){x=(ll)x*rev(b.x,M)%M;return *this;}
    mint operator/(mint b){mint res=*this;res/=b;return res;}
    mint operator^(ll w) {mint r=1,a=*this;while(w){if(w&1)r*=a;a*=a;w/=2;}return r;}
    mint operator^=(ll w){return *this=(*this)^w;}
    mint operator^(mint w){return *this^w.x;}
    mint operator^=(mint w){return *this=(*this)^w;}
    mint operator-()const{return mint()-*this;}
    explicit operator bool()const{return x;}
};
istream&operator>>(istream&is,mint&p){istream&res=is>>p.x;p.x%=M;return res;}
ostream&operator<<(ostream&os,mint p){return os<<p.x;}
template<typename T>mint operator+(T x,mint y){return mint(x)+y;}
template<typename T>mint operator-(T x,mint y){return mint(x)-y;}
template<typename T>mint operator*(T x,mint y){return mint(x)*y;}
template<typename T>mint operator/(T x,mint y){return mint(x)/y;}
template<typename T>mint operator^(T x,mint y){return mint(x)^y;}
mint abs(mint x){return x;}

const int N=303;
mint dp[N][N][N];
mint pr[N][N][N];
mint f(int i,int j,int l,int r){
    upn(r,N-1);
    return pr[i][j][r]-(l?pr[i][j][l-1]:0);
}
mint p2[N][N][N];
mint g(int i,int j,int b){
    if(b<0)return 0;
    return p2[i][j][b];
}
int32_t main(){
    string s;
    int k;
    cin>>s>>k;
    int n=sz(s);
    upn(k,n);
    vector<int> a;
    int cnt=0;
    for(char c:s){
        if(c=='0'){
            a.pb(cnt);
            cnt=0;
        }else{
            cnt++;
        }
    }
    a.pb(cnt);
    forn(j,k+1)dp[0][j][j]=1;
    for(int i=1;i<sz(a);++i){
        for(int j=0;j<N;++j){
            for(int b=0;b<N;++b){
                pr[i-1][j][b]=dp[i-1][j][b]+(b?pr[i-1][j][b-1]:0);
                p2[i-1][j][b]=dp[i-1][j][b]+((b&&j)?p2[i-1][j-1][b-1]:0);
            }
        }
        for(int j=0;j<=k;++j){
            for(int b=0;b<=j;++b){
                dp[i][j][b]=f(i-1,j,b,b+a[i]);
                dp[i][j][b]+=g(i-1,j-1,b-1);
            }
        }
    }
    mint ans=0;
    forn(j,k+1)ans+=dp[sz(a)-1][j][0];
    cout<<ans<<'\n';
    return 0;
}


Measured memory_bytes: 329624