// #include "pch.h"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <climits>
#include <string>
#include <cmath>
#include <bitset>
#include <complex>
#include <functional>
#include <ctime>
#include <cassert>
#include <fstream>
#include <stack>
#include <random>

typedef long long ll;
typedef std::pair<int, int> Pii;
typedef std::pair<long long, long long> Pll;
typedef std::pair<double, double> Pdd;

#define rip(i, n, s) for (int i = (s);i < (int)( n ); i++)
#define all(a) a.begin(), a.end()
#define MM << " " <<

template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template<typename T>
inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template<typename T>
inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<typename T>
void vdeb(std::vector<T> &da) {
    for (int i = 0;i < da.size();i++) {
        if (i == da.size() - 1) std::cout << da[i];
        else std::cout << da[i] << ' ';
    }
    std::cout << '\n';
}
template<typename T>
void vdeb(std::vector<std::vector<T>> &da) {
    for (int i = 0;i < da.size();i++) {
        std::cout << i << ' ';
        vdeb(da[i]);
    }
    std::cout << '\n';
}

long long pow(long long n, long long p, long long k) {//n^k(mod p)
    if (!k) return 1;
    long long a = pow(n,p, k>>1);
    a = a * a%p;
    if (k & 1) a = a * n%p;
    return a;
}
void euclid(long long &a, long long &b, long long p) { // a>=b A*b+B*(a-a/b*b)=1
    if (a == 1) {
        a = 1;
    }
    else {
        long long A = b, B = a % b;
        euclid(A, B, p);
        b = (A - (p + a / b) % p * B % p + p) % p;
        a = B;
    }
}
long long rev(long long n, long long p) {// n*x-p*y=1
    //long long q = p;
    //euclid(p, n, p);
    //return n % q;
    return pow(n,p,p-2);
}
long long bino(long long n, long long m, long long p) {//nCm(mod p)
    long long ans = 1, div = 1;
    for(int i = 0;i < m; i++){
        ans = (n - i) * ans % p;
        div = div * (i +1) % p;
    }
    return ans * rev(div, p) % p;
}
struct modint {
    long long num;
    long long p;
    modint() {
        num = 0;
        p = 998244353;
    }
    modint(long long x) {
        p = 998244353;
        num = x % p;
    }
    modint inv()const{return rev(num, p);}
    modint operator-() const{return modint(p-num);}
    modint& operator+=(const modint &other){
        num = (num + other.num) % p;
        return *this;
    }
    modint& operator-=(const modint &other){
        num = (num - other.num + p) % p;
        return *this;
    }
    modint& operator*=(const modint &other){
        num = (num * other.num) % p;
        return *this;
    }
    modint& operator/=(const modint &other){
        (*this) *= other.inv();
        return *this;
    }
    modint& operator+=(const long long &other){
        num = (num + other) % p;
        return *this;
    }
    modint& operator-=(const long long &other){
        num = (num - other + p) % p;
        return *this;
    }
    modint& operator*=(const long long &other){
        num = (num * other) % p;
        return *this;
    }
    modint& operator/=(const long long &other){
        (*this) *= rev(other, p);
        return *this;
    }
    modint& operator++(){return *this += 1;}
    modint& operator--(){return *this -= 1;}
    modint& operator=(const long long &other){return (*this) = modint(other);}
    modint operator+(const modint &other) const{return modint(*this) += other;}
    modint operator-(const modint &other) const{return modint(*this) -= other;}
    modint operator*(const modint &other) const{return modint(*this) *= other;}
    modint operator/(const modint &other) const{return modint(*this) /= other;}
    modint operator+(const long long &other) const{return modint(*this) += other;}
    modint operator-(const long long &other) const{return modint(*this) -= other;}
    modint operator*(const long long &other) const{return modint(*this) *= other;}
    modint operator/(const long long &other) const{return modint(*this) /= other;}
    bool operator==(const modint &other) const{return num == other.num;}
};
std::istream& operator>>(std::istream &is, const modint x) {
    std::cin >> x.num;
    return is;
}
std::ostream& operator<<(std::ostream &os, const modint &x){
    std::cout << x.num;
    return os;
}

using namespace std;

int main() {
    string s; cin >> s;
    int n = s.size(), k; cin >> k;
    vector<int> da(1);
    rip(i,n,0) {
        if(s[i] == '0') da.push_back(0);
        else ++da[da.size()-1];
    }
    chmin(k, n);
    ++k;
    vector<vector<vector<modint>>> dp(da.size()+1, vector<vector<modint>>(k+1, vector<modint>(k+1)));
    dp[0][0][0] += 1;
    rip(i,da.size(),0) {
        rip(j,k,0) {
            rip(l,k,0) {
                dp[i+1][j][l] += dp[i][j][l];
                dp[i+1][j+1][l] -= dp[i][j][l];
                dp[i+1][j][l] += dp[i][j][l];
                dp[i+1][j][l+1] -= dp[i][j][l];
                dp[i+1][min(l, j+da[i])+1][l] -= dp[i][j][l];
                dp[i+1][min(l, j+da[i])+1][l+1] += dp[i][j][l];
            }
        }
        rip(j,k+1,0) rip(l,k,0) dp[i+1][j][l+1] += dp[i+1][j][l];
        rip(j,k,0) rip(l,k+1,0) dp[i+1][j+1][l] += dp[i+1][j][l];
        rip(j,k+1,0) rip(l,k+1,0) dp[i+1][j][l] -= dp[i][j][l];
    }
    modint ans;
    rip(i,k,0) ans += dp.back()[i][i];
    cout << ans << endl;
}

Measured memory_bytes: 221560