#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define elif else if
#define sp(x) fixed << setprecision(x)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const ll MOD = 1e9+7;
const ll MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
const ld EPS = 1e-10;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};

template<ll mod> struct Mod_Int{
    ll x;
    Mod_Int() {}
    Mod_Int(ll y) : x (y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    Mod_Int &operator += (const Mod_Int &p) {
        x = (x + p.x) % mod;
        return *this;
    }

    Mod_Int &operator -= (const Mod_Int &p) {
        x = (x + mod - p.x) % mod;
        return *this;
    }

    Mod_Int &operator *= (const Mod_Int &p) {
        x = (x * p.x) % mod;
        return *this;
    }

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

    Mod_Int &operator ++ () {return *this += (Mod_Int)1;}

    Mod_Int operator ++ (int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator -- () {return *this -= (Mod_Int)1;}

    Mod_Int operator -- (int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

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

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

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

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

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

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

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

    Mod_Int pow (ll n) const {
        Mod_Int now = *this, ret = 1;
        while(n > 0){
            if(n & 1) ret *= now;
            now *= now, n >>= 1;
        }
        return ret;
    }

    Mod_Int inverse () const {
        return pow(mod-2);
    }
};

using mint = Mod_Int<MOD>;
const int MAX_N = 1e6;
mint fac[MAX_N+1], ifac[MAX_N+1];

void init(){
    fac[0] = 1;
    rep2(i, 1, MAX_N){
        fac[i] = fac[i-1]*i;
    }
    ifac[MAX_N] = fac[MAX_N].inverse();
    rep3(i, MAX_N, 1){
        ifac[i-1] = ifac[i]*i;
    }
}

mint comb(int n, int k){
    return fac[n]*ifac[n-k]*ifac[k];
}

mint perm(int n, int k){
    return fac[n]*ifac[n-k];
}

int main(){
    string S;
    int K;
    cin >> S >> K;
    int n = 1, N = sz(S), cnt = 0;
    rep(i, N){
        if(S[i] == '0') n++;
        else cnt++;
    }
    vector<int> a;
    int x = 0;
    while(x < N && S[x] == '1') x++;
    a.pb(x);
    rep(i, N){
        if(S[i] == '1') continue;
        int j = 1;
        while(i+j < N && S[i+j] == '1') j++;
        a.pb(j-1);
    }
    //for(auto &e: a) cout << e << ' '; cout << endl;
    //cout << n << ' ' << cnt << endl;
    chmin(K, N);
    mint dp[n+1][K+1][cnt+1];
    rep(i, n+1) rep(j, K+1) rep(k, cnt+1) dp[i][j][k] = 0;
    dp[0][0][0] = 1;
    int sum = 0;
    rep(i, n){
        sum += a[i];
        rep(j, K+1){
            rep(k, cnt+1){
                rep(l, cnt+1){
                    if(k+l > cnt) break;
                    int tmp = max(0, l-a[i]);
                    if(k+l < sum) continue;
                    if(j+tmp > K) continue;
                    dp[i+1][j+tmp][k+l] += dp[i][j][k];
                }
            }
        }
    }
    mint ans = 0;
    rep(j, K+1) ans += dp[n][j][cnt];
    cout << ans.x << endl;
}

Measured memory_bytes: 56940