//#include <bits/stdc++.h>
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;


#include "boost/multiprecision/cpp_int.hpp"
#include "boost/multiprecision/cpp_dec_float.hpp"
namespace mp = boost::multiprecision;
typedef mp::cpp_int LL;
typedef mp::number<mp::cpp_dec_float<1024>> DD;// 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする)

 
typedef long double dd;
//#define i_7 (ll)(1E9+7)
#define i_7 998244353
#define i_5 i_7-2
ll mod(ll a){
    ll c=a%i_7;
    if(c>=0)return c;
    return c+i_7;
}
typedef pair<ll,ll> l_l;
typedef pair<dd,dd> d_d;
ll inf=(ll)1E16;
#define rep(i,l,r) for(ll i=l;i<=r;i++)
#define rrep(i,r,l) for(ll i=r;i>=l;i--)
#define pb push_back
ll max(ll a,ll b){if(a<b)return b;else return a;}
ll min(ll a,ll b){if(a>b)return b;else return a;}
void Max(ll &pos,ll val){pos=max(pos,val);}//Max(dp[n],dp[n-1]);
void Min(ll &pos,ll val){pos=min(pos,val);}
void Add(ll &pos,ll val){pos=mod(pos+val);}
dd EPS=1E-9;
#define fastio ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define fi first
#define se second
#define endl "\n"  //インタラクティブで消す！！！！！！！！！！！！！！！！！！！！！
#define SORT(v) sort(v.begin(),v.end())
#define ERASE(v) v.erase(unique(v.begin(),v.end()),v.end())
#define POSL(v,x) (lower_bound(v.begin(),v.end(),x)-v.begin())
#define POSU(v,x) (upper_bound(v.begin(),v.end(),x)-v.begin())
template<class T,class S>
inline bool chmax(T &a, S b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}
template<class T,class S>
inline bool chmin(T &a, S b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

void mod_print(ll k){
    ll P=1000;
    rep(y,1,P){
        ll x=mod(y*k);
        if(x+P>=i_7){
            x-=i_7;
        }
        if(abs(x)<=P){
            //cout<<x<<"/"<<y;
            cout<<setprecision(5)<<(dd)x/(dd)y;
            return;
        }
    }
    cout<<"nun"<<endl;
}
#define all(c) c.begin(),c.end()
//////////////////////////


int main(){fastio
    string s;
    ll lim;
    cin>>s>>lim;
    ll ssz=s.size();
    ll n=0;
    ll m=0;
    rep(i,0,ssz-1){
        if(s[i]=='0')n++;
        else m++;
    }
    ll cnt[n+1];memset(cnt,0,sizeof(cnt));
    ll ze=0;
    rep(i,0,ssz-1){
        if(s[i]=='0')ze++;
        else cnt[ze]++;
    }
    //rep(i,0,n)cout<<cnt[i]<<" ";cout<<endl;
    ll csum[n+1];
    rrep(i,n,0){
        if(i==n)csum[i]=cnt[i];
        else csum[i]=csum[i+1]+cnt[i];
    }
   // rep(i,0,n)cout<<csum[i]<<" ";cout<<endl;
    
    chmin(lim,m+1);
    //ll N=10;
    ll N=305;
    ll dp[n+1][m+1][lim+1];memset(dp,0,sizeof(dp));
    ll ep[n+1][m+1][lim+1];memset(ep,0,sizeof(ep));
    ll fp[n+1][N*2][lim+1];memset(fp,0,sizeof(fp));
    rep(j,0,cnt[n])dp[n][j][0]=1;
    rrep(i,n-1,-1){
        rep(k,0,lim){
            rep(j,0,m){
                if(j==0)ep[i+1][j][k]=dp[i+1][j][k];
                else ep[i+1][j][k]=mod(dp[i+1][j][k]+ep[i+1][j-1][k]);
            }
        }
        rep(dis,0,N*2-1){
            rep(k,0,lim){
                ll j=dis+k-N;
                if(j<0||j>m)continue;
                if(k==0)fp[i+1][dis][k]=dp[i+1][j][k];
                else fp[i+1][dis][k]=mod(fp[i+1][dis][k-1]+dp[i+1][j][k]);
            }
        }
        /*
        rep(j,0,m){
            rep(k,0,lim){
                cout<<dp[i+1][j][k]<<" ";
            }cout<<endl;
        }cout<<endl;
        rep(j,0,m){
            rep(k,0,lim){
                cout<<ep[i+1][j][k]<<" ";
            }cout<<endl;
        }cout<<endl<<endl;
        rep(j,0,N*2-1){
            rep(k,0,lim){
                cout<<fp[i+1][j][k]<<" ";
            }cout<<endl;
        }cout<<endl<<endl;
        */
        if(i==-1)break;
        
        rep(j,0,csum[i]){
            rep(k,0,lim){
                /*
                rep(p,0,csum[i]){
                    if(j-p<0)continue;
                    if(p<=cnt[i])Add(dp[i][j][k],dp[i+1][j-p][k]);
                    else{
                        ll oldk=k-(p-cnt[i]);
                        if(oldk<0||lim<oldk)continue;
                        Add(dp[i][j][k],dp[i+1][j-p][oldk]);
                    }
                }
                */
                ll add=ep[i+1][j][k];
                if(j-cnt[i]-1>=0)Add(add,-ep[i+1][j-cnt[i]-1][k]);
                Add(dp[i][j][k],add);
                
                ll OJ=j-cnt[i]-k+N;
                if(OJ<0||OJ>=2*N)continue;
                if(k>=1){
                    
                    add=fp[i+1][OJ][k-1];
                    
                    ll oldk=k+cnt[i]-csum[i]-1;
                    if(0<=oldk&&oldk<=lim)Add(add,-fp[i+1][OJ][oldk]);
                    
                    Add(dp[i][j][k],add);
                }
            }
        }
    }
    
    /*rep(i,0,n){
        rep(j,0,m){
            rep(k,0,lim){
                cout<<dp[i][j][k]<<" ";
            }cout<<endl;
        }cout<<endl;
    }*/
    
    ll ans=0;
    rep(k,0,lim)Add(ans,dp[0][m][k]);
    
    cout<<ans<<endl;
    
    
    return 0;
}




Measured memory_bytes: 165544