#include <bits/stdc++.h>
    #include <ext/pb_ds/assoc_container.hpp>
    #include <ext/pb_ds/tree_policy.hpp>
    #define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>   
    using namespace std;
    using namespace __gnu_pbds;
    typedef long long ll; 
    #define int long long
    typedef unsigned long long lu;
    typedef vector<ll> v;
    typedef vector<vector<ll> > vv;
    typedef vector<string>  vs;
    typedef vector<pair<ll,ll>> vpr;
    typedef vector<bool>vb;
    typedef vector<double>vd;
    typedef long double ld;
    #define f(i,n) for(ll i = 0; i < n; i++)
    #define ff(i,n) for(ll i=1;i<=n;i++)
    #define pb push_back
    #define mp make_pair
    #define endl "\n"
    #define fi first
    #define se second
    #define all(x) x.begin(),x.end()
    #define rall(x) x.rbegin(),x.rend()
    #define amax(x,y) if(y>x) x=y;
    #define amin(x,y) if(y<x)x=y;
    #define bg(x) x.begin()
    #define sz(x) (ll)x.size()
    #define in(x,n) for(ll i=0;i<n;i++)cin>>x[i]
    #define out(x,n) for(ll i=0;i<n;i++)cout<<x[i]<<" " 
    #define mxt(a) *(max_element(a.begin(),a.end()))
    #define mnt(a) *(min_element(a.begin(),a.end())
    #define tc ll t;cin>>t;while(t--)
    typedef pair<ll,ll> pi;
    #define yes cout<<"YES\n";
    #define no cout<<"NO\n";
    #define yesno(f) if(f) yes else no
    const v dx = {1, -1, 0, 0};
    const v dy = {0, 0, 1, -1};
    const ld PI = 2 * acos(0.0);
    ll cel(ll x1,ll y1){if((x1%y1)==0)return x1/y1;else return x1/y1+1;}
    ll power(ll a,ll b,ll m)
    {
        if(b==0)
            return 1;
        ll d=power(a,b/2,m);
        d=(d*d)%m;
        if(b&1)
            d=(d*a)%m;
        return d;
    }
    const ll mod=998244353;
    int MOD(int a)
    {
        if(a<0)
            a+=mod;
        if(a>=mod)
            a%=mod;
        return a;
    }
    // set_name.find_by_order(k) It returns to an iterator to the kth element (counting from zero) in the set in O(logn) time
    // set_name.order_of_key(k) It returns to the number of items that are strictly smaller than our item k in O(logn) time.
    /*string operations :
    str.substr (x,y) : returns a substring str[x],str[x+1],...str[x+y-1]
    str.substr (x) : returns a substring str[x],... end of string
    str.find(qtr) : returns the first occurenece of qtr in str */
    int dp[301][301][301],pre[301][301][301];
    int32_t main()
    {
        ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
        // freopen("input.txt", "r", stdin);
        // freopen("output.txt", "w", stdout);
        string s;cin>>s;
        int kmax;cin>>kmax;
        kmax=min(kmax,sz(s));
        int n=sz(s);
        v vec;
        for(int i=0;i<n;i++)
        {
            if(s[i]=='0')
                vec.pb(i);
        }
        if(sz(vec)==0)
        {
            cout<<1<<endl;
            return 0;
        }
        v my_count(sz(vec));
        for(int i=0;i<sz(vec)-1;i++)
        {
            my_count[i]=vec[i+1]-vec[i]-1;
        }
        my_count[sz(vec)-1]=n-1-vec.back();
        int jmax=n-sz(vec);
        int imax=sz(vec)-1;
        for(int k=kmax;k>=0;k--)
        {
            for(int i=0;i<=imax;i++)
            {
                if(i==0)
                {
                    for(int j=0;j<=jmax;j++)
                    {
                        dp[i][j][k]=j+1+min(my_count[i],kmax-k);
                    }
                    for(int j=0;j<=jmax;j++)
                    {
                        if(j!=0)
                        pre[i][j][k]=MOD(pre[i][j-1][k]+dp[i][j][k]);
                        else
                            pre[i][j][k]=dp[i][j][k];
                    }
                    continue;
                }
                for(int j=0;j<=jmax;j++)
                {
                    for(int count=0;count<=my_count[i];count++)
                    {
                        if(k+count >kmax || j+count > jmax)
                            break;
                        dp[i][j][k]+=dp[i-1][j+count][k+count];
                        dp[i][j][k]=MOD(dp[i][j][k]);
                    }
                    if(j>=1)
                    {
                        dp[i][j][k]+=pre[i-1][j-1][k];
                        dp[i][j][k]=MOD(dp[i][j][k]);
                    }
                }
                for(int j=0;j<=jmax;j++)
                {
                    if(j!=0)
                    pre[i][j][k]=MOD(pre[i][j-1][k]+dp[i][j][k]);
                    else
                        pre[i][j][k]=dp[i][j][k];
                }
            }
        }
        cout<<dp[imax][0][0]<<endl;

        return 0;
    }

Measured memory_bytes: 110840