// #define _GLIBCXX_DEBUG // for STL debug (optional)
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>
using namespace std;
using ll = long long int;
using int64 = long long int;
 
template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}
 
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const int INF = 1LL << 29;
const ll LONGINF = 1LL << 60;
const ll MOD =  998244353LL;

// ModInt begin

using ll = long long;
template<ll mod>
struct ModInt {
    ll v;
    ll mod_pow(ll x, ll n) const {
        return (!n) ? 1 : (mod_pow((x*x)%mod,n/2) * ((n&1)?x:1)) % mod;
    }
    ModInt(ll a = 0) : v((a %= mod) < 0 ? a + mod : a) {}
    ModInt operator+ ( const ModInt& b ) const {
        return (v + b.v >= mod ? ModInt(v + b.v - mod) : ModInt(v + b.v));
    }
    ModInt operator- () const {
        return ModInt(-v);
    }
    ModInt operator- ( const ModInt& b ) const {
        return (v - b.v < 0 ? ModInt(v - b.v + mod) : ModInt(v - b.v));
    }
    ModInt operator* ( const ModInt& b ) const {return (v * b.v) % mod;}
    ModInt operator/ ( const ModInt& b ) const {return (v * mod_pow(b.v, mod-2)) % mod;}
    
    bool operator== ( const ModInt &b ) const {return v == b.v;}
    bool operator!= ( const ModInt &b ) const {return !(*this == b); }
    ModInt& operator+= ( const ModInt &b ) {
        v += b.v;
        if(v >= mod) v -= mod;
        return *this;
    }
    ModInt& operator-= ( const ModInt &b ) {
        v -= b.v;
        if(v < 0) v += mod;
        return *this;
    }
    ModInt& operator*= ( const ModInt &b ) {
        (v *= b.v) %= mod;
        return *this;
    }
    ModInt& operator/= ( const ModInt &b ) {
        (v *= mod_pow(b.v, mod-2)) %= mod;
        return *this;
    }
    ModInt pow(ll x) { return ModInt(mod_pow(v, x)); }
    // operator int() const { return int(v); }
    // operator long long int() const { return v; }
};

template<ll mod>
ModInt<mod> pow(ModInt<mod> n, ll k) {
    return ModInt<mod>(n.mod_pow(n.v, k));
}

template<ll mod>
ostream& operator<< (ostream& out, ModInt<mod> a) {return out << a.v;}
template<ll mod>
istream& operator>> (istream& in, ModInt<mod>& a) {
    in >> a.v;
    return in;
}

// ModInt end

using mint = ModInt<MOD>;
mint dp[310][310][310];
int main() {
    string s; cin >> s;
    int K; cin >> K;
    {
        int cnt = count(s.begin(), s.end(), '0');
        if(cnt == 0 or cnt == s.size()) {
            puts("1");
            return 0;
        }
    }

    reverse(s.begin(), s.end()); s += "0";
    int N = s.size(); K = min(K, N);
    vector<int> ones;
    {
        int cnt = 0;
        for(int i=0; i<N; i++) {
            if(s[i] == '1') cnt++;
            if(s[i] == '0') {
                ones.emplace_back(cnt);
                cnt = 0;
            }
        }
    }
    for(auto one : ones) cerr << one << " ";
    cerr << endl;

    int M = ones.size(), ones_sum = 0;
    dp[0][0][0] = mint(1);
    for(int t=0; t<M; t++) {
        mint tmp[310][310];
        fill(tmp[0], tmp[305], mint(0));
        
        for(int i=0; i<=ones_sum; i++) {
            for(int k=0; k<=K; k++) {
                // (j-i-ones[t] <= 0) -> (j <= i+ones[t])
                // i から i+ones[t] まではノーコストで遷移可能
                // i+ones[t]+1 から ones_sum+ones[t] までは 1 ずつ増えてく
                
                // ノーコスト遷移
                {
                    dp[t+1][i][k] += dp[t][i][k];
                    dp[t+1][i+ones[t]][k] -= dp[t][i][k];
                }
                // 1 ずつ増える遷移
                int c = min(K-k, ones_sum-i);
                {
                    tmp[i+ones[t]][k] += dp[t][i][k];
                    tmp[i+ones[t]+c+1][k+c+1] -= dp[t][i][k];
                }                
            }
        }
        for(int j=0; j<=N; j++) {
            for(int k=0; k<=K; k++) {
                tmp[j+1][k+1] += tmp[j][k];
            }
        }
        for(int j=0; j<=N; j++) {
            for(int k=0; k<=K; k++) {
                if(j > 0) dp[t+1][j][k] += dp[t+1][j-1][k];
            }
        }
        for(int j=0; j<=N; j++) {
            for(int k=0; k<=K; k++) {
                dp[t+1][j][k] += tmp[j][k];
            }
        }
        ones_sum += ones[t];
    }
    
    mint ans(0);
    for(int i=0; i<=K; i++) ans += dp[M][ones_sum][i];
    cout << ans << endl;
    return 0;
}


Measured memory_bytes: 237124