#include <bits/stdc++.h>
using namespace std;
#define rep(i, n)  for(long long i=0;i<(long long)(n);i++)
#define REP(i,k,n) for(long long i=k;i<(long long)(n);i++)
#define all(a) a.begin(),a.end()
#define pb emplace_back
#define eb emplace_back
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
#define ub(v,k) (upper_bound(all(v),k)-v.begin())
#define fi first
#define se second
#define pi M_PI
#define PQ(T) priority_queue<T>
#define SPQ(T) priority_queue<T,vector<T>,greater<T>>
#define dame(a) {out(a);return 0;}
#define decimal cout<<fixed<<setprecision(15);
#define dupli(a) a.erase(unique(all(a)),a.end())
typedef long long ll;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef tuple<ll,ll,ll,ll> PPP;
typedef multiset<ll> S;
using vi=vector<ll>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vvvvi=vector<vvvi>;
using vp=vector<P>;
using vvp=vector<vp>;
using vb=vector<bool>;
using vvb=vector<vb>;
const ll inf=1001001001001001001;
const ll INF=1001001001;
const ll mod=998244353;
const double eps=1e-10;
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outp(T a){cout<<'('<<a.fi<<','<<a.se<<')'<<'\n';}
template<class T> void outvp(T v){rep(i,v.size())cout<<'('<<v[i].fi<<','<<v[i].se<<')';cout<<'\n';}
template<class T> void outvvp(T v){rep(i,v.size())outvp(v[i]);}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
template<class T> void outvv(T v){rep(i,v.size())outv(v[i]);}
template<class T> bool isin(T x,T l,T r){return (l)<=(x)&&(x)<=(r);}
template<class T> void yesno(T b){if(b)out("yes");else out("no");}
template<class T> void YesNo(T b){if(b)out("Yes");else out("No");}
template<class T> void YESNO(T b){if(b)out("YES");else out("NO");}
template<class T> void noyes(T b){if(b)out("no");else out("yes");}
template<class T> void NoYes(T b){if(b)out("No");else out("Yes");}
template<class T> void NOYES(T b){if(b)out("NO");else out("YES");}
void outs(ll a,ll b){if(a>=inf-100)out(b);else out(a);}
ll gcd(ll a,ll b){if(b==0)return a;return gcd(b,a%b);}
ll modpow(ll a,ll b){ll res=1;a%=mod;while(b){if(b&1)res=res*a%mod;a=a*a%mod;b>>=1;}return res;}
int main(){
    string s;cin>>s;
    ll k;cin>>k;
    chmin(k,(ll)(s.size()+3));
    k++;
    vi v(1);
    ll id=0;
    rep(i,s.size()){
        if(s[i]=='0'){
            id++;
            v.pb(0);
        }
        else v[id]++;
    }
    ll n=v.size();
    vvi dp(k,vi(s.size()+1));
    dp[0][0]=1;
    for(int i=n-1;i>=0;i--){
        vvi ndp(k,vi(s.size()+1));
        vvi rui=dp;
        rep(j,k)rep(t,s.size()){
            rui[j][t+1]=(rui[j][t+1]+rui[j][t])%mod;
        }
        vvi r(k+s.size(),vi(k));
        rep(j,k)rep(t,s.size()+1){
            r[j+t][j]=dp[j][t];
        }
        rep(j,k+s.size())rep(t,k-1){
            r[j][t+1]+=r[j][t];
            r[j][t+1]%=mod;
        }
        rep(j,k)rep(t,s.size()+1){
            ndp[j][t]=rui[j][t];
            if(t-v[i]-1>=0)ndp[j][t]-=rui[j][t-v[i]-1];
            if(j)ndp[j][t]+=r[j+t][j-1];
            ndp[j][t]%=mod;
            ndp[j][t]=(ndp[j][t]+mod)%mod;
        }
        dp=ndp;
    }
    ll ans=0;
    rep(i,k)ans+=dp[i][0];
    ans%=mod;
    out(ans);
}

Measured memory_bytes: 6880