//header
#ifdef LOCAL
    #include "/Users/takakurashokichi/Desktop/atcoder/cxx-prettyprint-master/prettyprint.hpp"
    #define debug(x) cout << x << endl
#else
    #define debug(...) 42
#endif
    #pragma GCC optimize("Ofast")
    #include <bits/stdc++.h>
    //types
    using namespace std;
    using ll = long long;
    using ull = unsigned long long;
    using ld = long double;
    typedef pair < ll , ll > Pl;        
    typedef pair < int, int > Pi;
    typedef vector<ll> vl;
    typedef vector<int> vi;
    typedef vector<char> vc;
    template< typename T >
    using mat = vector< vector< T > >;
    typedef vector<vector<int>> vvi;
    typedef vector<vector<long long>> vvl;
    typedef vector<vector<char>> vvc;

    template< int mod >
    struct modint {
        int x;

        modint() : x(0) {}

        modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

        modint &operator+=(const modint &p) {
            if((x += p.x) >= mod) x -= mod;
            return *this;
        }

        modint &operator-=(const modint &p) {
            if((x += mod - p.x) >= mod) x -= mod;
            return *this;
        }

        modint &operator*=(const modint &p) {
            x = (int) (1LL * x * p.x % mod);
            return *this;
        }

        modint &operator/=(const modint &p) {
            *this *= p.inverse();
            return *this;
        }

        modint operator-() const { return modint(-x); }

        modint operator+(const modint &p) const { return modint(*this) += p; }

        modint operator-(const modint &p) const { return modint(*this) -= p; }

        modint operator*(const modint &p) const { return modint(*this) *= p; }

        modint operator/(const modint &p) const { return modint(*this) /= p; }

        bool operator==(const modint &p) const { return x == p.x; }

        bool operator!=(const modint &p) const { return x != p.x; }

        modint inverse() const {
            int a = x, b = mod, u = 1, v = 0, t;
            while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
            }
            return modint(u);
        }

        modint pow(int64_t n) const {
            modint ret(1), mul(x);
            while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
            }
            return ret;
        }

        friend ostream &operator<<(ostream &os, const modint &p) {
            return os << p.x;
        }

        friend istream &operator>>(istream &is, modint &a) {
            int64_t t;
            is >> t;
            a = modint< mod >(t);
            return (is);
        }

        static int get_mod() { return mod; }
    };
    //abreviations
    #define all(x) (x).begin(), (x).end()
    #define rall(x) (x).rbegin(), (x).rend()
    #define rep_(i, a_, b_, a, b, ...) for (int i = (a), max_i = (b); i < max_i; i++)
    #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
    #define rrep_(i, a_, b_, a, b, ...) for (int i = (b-1), min_i = (a); i >= min_i; i--)
    #define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
    #define SZ(x) ((int)(x).size())
    #define pb(x) push_back(x)
    #define eb(x) emplace_back(x)
    #define mp make_pair
    #define print(x) cout << x << endl
    #define vprint(x) rep(i, x.xize())cout << x[i] << ' '; cout << endl
    #define vsum(x) accumulate(all(x), 0LL)
    #define vmax(a) *max_element(all(a))
    #define vmin(a) *min_element(all(a))
    #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
    #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
    //functions
    //gcd(0, x) fails.
    ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
    ll lcm(ll a, ll b) { return a/gcd(a, b)*b;}
    template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
    template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
    template< typename T >
    T mypow(T x, ll n) {
        T ret = 1;
        while(n > 0) {
            if(n & 1) (ret *= x);
            (x *= x);
            n >>= 1;
        }
        return ret;
    }
    ll modpow(ll x, ll n, const ll mod) {
        ll ret = 1;
        while(n > 0) {
            if(n & 1) (ret *= x);
            (x *= x);
            n >>= 1;
            x%=mod;
            ret%=mod;
        }
        return ret;
    }
    uint64_t my_rand(void) {
        static uint64_t x = 88172645463325252ULL;
        x = x ^ (x << 13); x = x ^ (x >> 7);
        return x = x ^ (x << 17);
    }
    int popcnt(ull x) { return __builtin_popcountll(x); } 
    //graph template
    template< typename T >
    struct edge {
        int src, to;
        T cost;

        edge(int to, T cost) : src(-1), to(to), cost(cost) {}

        edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

        edge &operator=(const int &x) {
            to = x;
            return *this;
        }
        operator int() const { return to; }
    };
    template< typename T >
    using Edges = vector< edge< T > >;
    template< typename T >
    using WeightedGraph = vector< Edges< T > >;
    using UnWeightedGraph = vector< vector< int > >;
    struct Timer { 
        clock_t start_time; 
        void start() {
            start_time = clock(); 
        }
        int lap() { 
            //return x ms.
            return (clock()-start_time)*1000 / CLOCKS_PER_SEC; 
        }
    };
//constant
//#define inf 1000000005LL
#define inf 4000000005LL
#define INF 4000000004000000000LL
#define mod 998244353LL
#define endl '\n'
typedef modint<mod> mint;
const long double eps = 0.000001;
const long double PI  = 3.141592653589793;
//library
int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << setprecision(20);
    string x; int k;
    cin>>x>>k;
    int n = x.size();
    vector<char> s(n);
    rep(i, n)s[i] = x[n-1-i];
    //int m = min(k, n);
    //iばんめ, j個あまり, p回使った;
    vector<mat<mint>> dp(n+5, mat<mint>(n+5, vector<mint>(n+5)));
    vi id;
    int cnt = 0;
    vi ones;
    rep(i, n){
        if(s[i]=='0'){
            ones.pb(cnt);
            cnt = 0;
        }else{
            cnt++;
        }
    }
    ones.pb(cnt);
    int l = ones.size();
    rep(i, ones[0]+1){
        dp[0][ones[0]-i][0] = 1;
    }
    rep(i, 1, l){
        rep(p, n+1){
            //[s-ones[i], s]
            mint sm = 0;
            rep(s, n+1){
                sm+=dp[i-1][s][p];
                dp[i][s][p]+=sm;
                if(s>=ones[i]){
                    sm-=dp[i-1][s-ones[i]][p];//?
                }
            }
        }
        vector<mint> sm(n*2+2);
        rep(xx, n*2+2){
            rep(yy, xx+1){
                if(xx>n||(xx-yy)>n)continue;
                sm[xx]+=dp[i-1][yy][xx-yy];
            }
        }
        rrep(p, n+1){
            rrep(s, n+1){
                dp[i][s][p]+=sm[s+p]-dp[i-1][s][p];
                sm[s+p]-=dp[i-1][s][p];
            }
        }
    }
    print(accumulate(dp[l-1][0].begin(), dp[l-1][0].begin()+min(n, k)+1, (mint)0));
   //debug(dp[3]);
}


Measured memory_bytes: 117764