#include <bits/stdc++.h>
 
//    #include <boost/multiprecision/cpp_int.hpp>
 #define int long long
// #define inf  1000000007
 #define inf  998244353

 #define pa pair<int,int>
 #define ll long long
 #define pal pair<double,double>
 #define ppap pair<pa,int>
  #define PI 3.14159265358979323846
  #define paa pair<int,char>
  #define  mp make_pair
  #define  pb push_back
  #define EPS (1e-8)
                                          
    int dx[8]={0,1,0,-1,1,1,-1,-1};
    int dy[8]={1,0,-1,0,-1,1,1,-1};
                                            using namespace std;
                                   			class pa3{
                                            	public:
                                            	int x;
                                   				int y,z;
                                            	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                            	bool operator < (const pa3 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		 return z<p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                   				bool operator > (const pa3 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		 return z>p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa3 &p) const{
                                            		return x==p.x && y==p.y && z==p.z;
                                            	}
                                            		bool operator != (const pa3 &p) const{
                                            			return !( x==p.x && y==p.y && z==p.z);
                                            	}
                                            
                                            };
                                            
                                            class pa4{
                                            	public:
                                            	int x;
                                            	int y,z,w;
                                            	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                            	bool operator < (const pa4 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		if(z!=p.z)return z<p.z;
                                            		return w<p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator > (const pa4 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		if(z!=p.z)return z>p.z;
                                            		return w>p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa4 &p) const{
                                            		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                            	}
                                            		
                                            
                                            };
                                            class pa2{
                                            	public:
                                            	int x,y;
                                            	pa2(int x=0,int y=0):x(x),y(y) {}
                                            	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                            	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                            	bool operator < (const pa2 &p) const{
                                            		return y != p.y ? y<p.y: x<p.x;
                                            	}
                                            	bool operator > (const pa2 &p) const{
                                            		return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa2 &p) const{
                                            		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                            	}
                                            	bool operator != (const pa2 &p) const{
                                            		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                            	}
                                            		
                                            
                                            };
                                            
 
                      
                                string itos( int i ) {
                                ostringstream s ;
                                s << i ;
                                return s.str() ;
                                }
                                 
                                int Gcd(int v,int b){
                                	if(v==0) return b;
                                	if(b==0) return v;
                                	if(v>b) return Gcd(b,v);
                                	if(v==b) return b;
                                	if(b%v==0) return v;
                                	return Gcd(v,b%v);
                                }
                 
                            
                                int mod;
int extgcd(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int d = extgcd(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
pa operator+(const pa & l,const pa & r) {   
    return {l.first+r.first,l.second+r.second};                                    
}    
pa operator-(const pa & l,const pa & r) {   
    return {l.first-r.first,l.second-r.second};                                    
}  
                int beki(int wa,int rr,int warukazu){
                	if(rr==0) return 1%warukazu;
                	if(rr==1) return wa%warukazu;
                	wa%=warukazu;
                	if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
                	ll zx=beki(wa,rr/2,warukazu);
                	return (zx*zx)%warukazu;
                }
 
                              
                int pr[1000100];
                int inv[1000010];
                

                
    			int comb(int nn,int rr){
    				if(rr<0 || rr>nn || nn<0) return 0;
    				int r=pr[nn]*inv[rr];
    				r%=mod;
    				r*=inv[nn-rr];
    				r%=mod;
    				return r;
    			}
               
                void gya(int ert){
                	pr[0]=1;
                	for(int i=1;i<=ert;i++){
                		pr[i]=((ll)pr[i-1]*i)%mod;
                	}
                		inv[ert]=beki(pr[ert],mod-2,mod);
                	for(int i=ert-1;i>=0;i--){
                		inv[i]=(ll)inv[i+1]*(i+1)%mod;
                	}
                }
                
              //   cin.tie(0);
    		//	ios::sync_with_stdio(false);
    			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                 //sort(ve.begin(),ve.end(),greater<int>());
 //   mt19937(clock_per_sec);
  //  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;

int dp[315][315][315]={};

int memo1[320][320]={};
int memo2[320][320]={};

signed main(){
	mod=998244353;
	cin.tie(0);
	ios::sync_with_stdio(false);
	vector<int> ve(400,0);
	vector<int> rui(400,0);
	int cnt=1;
	int iti=0;
	int K;
	string s;
	cin>>s>>K;
	for(auto c:s){
		if(c=='0')cnt++;
		else ve[cnt]++,iti++;
	}
	for(int i=1;i<400;i++)rui[i]=ve[i]+rui[i-1];
	
	dp[0][0][0]=1;

	//int n=s.length();
	for(int i=0;i<cnt;i++){

		
		for(int j=0;j<=iti;j++)for(int p=0;p<=iti;p++)if(dp[i][j][p]){
	//	cout<<i<<" "<<j<<" "<<p<<"  "<<dp[i][j][p]<<endl;
		//cout<<j<<" "<<rui[i]<<endl;
		int sai=rui[i+1]-j;
		if(sai<0)sai=0;
		/*
		for(int k=sai;k+j<=iti;k++){
			cout<<"   "<<i+1<<" "<<j+k<<" "<<max(k,ve[i+1])-ve[i+1]+p<<endl;
			dp[i+1][j+k][max(k,ve[i+1])-ve[i+1]+p]+=dp[i][j][p];
			dp[i+1][j+k][max(k,ve[i+1])-ve[i+1]+p]%=mod;
		}
		*/
		int l=sai,r=iti-j;
		if(l>r)continue;
		if(l<=ve[i+1] && ve[i+1]<=r){
			memo1[j+l][p]+=dp[i][j][p];
			memo1[j+ve[i+1]+1][p]+=mod-dp[i][j][p];
			memo1[j+l][p]%=mod;
			memo1[j+ve[i+1]+1][p]%=mod;
			memo2[j+ve[i+1]+1][ve[i+1]+1-ve[i+1]+p]+=dp[i][j][p];
			memo2[j+r+1][r+1-ve[i+1]+p]+=mod-dp[i][j][p];
			memo2[j+ve[i+1]+1][ve[i+1]+1-ve[i+1]+p]%=mod;
			memo2[j+r+1][r+1-ve[i+1]+p]%=mod;

		}
		else if(ve[i+1]<l){
			memo2[j+l][l-ve[i+1]+p]+=dp[i][j][p];
			memo2[j+r+1][r+1-ve[i+1]+p]+=mod-dp[i][j][p];
			memo2[j+l][l-ve[i+1]+p]%=mod;
			memo2[j+r+1][r+1-ve[i+1]+p]%=mod;			
		}
			else{
			memo1[j+l][p]+=dp[i][j][p];
			memo1[j+r+1][p]+=mod-dp[i][j][p];
			memo1[j+l][p]%=mod;
			memo1[j+r+1][p]%=mod;
			
			}
		}
		
		
		
		
		for(int xi=0;xi<=310;xi++)for(int xj=0;xj<=310;xj++){
			if(xi){
				memo1[xi][xj]+=memo1[xi-1][xj];
				memo1[xi][xj]%=mod;
			}
			if(xi>0&&xj>0){
				memo2[xi][xj]+=memo2[xi-1][xj-1];
				memo2[xi][xj]%=mod;	
			}
		}
		for(int xi=0;xi<=310;xi++)for(int xj=0;xj<=310;xj++){
			dp[i+1][xi][xj]=(memo1[xi][xj]+memo2[xi][xj])%mod;
			memo1[xi][xj]=0;
			memo2[xi][xj]=0;
			
		}
		
		
	}
	int ans=0;
	for(int p=0;p<=min(K,310ll);p++){
//		cout<<cnt<<" "<<iti<<" "<<p<<"  "<<dp[cnt][iti][p]<<endl;
		
		ans+=dp[cnt][iti][p];
		ans%=mod;
	}
	cout<<ans<<endl;
	return 0;
 }


Measured memory_bytes: 235880