#include <bits/stdc++.h>
using namespace std;
using lint = long long;
constexpr lint mod = 998244353;
#define all(x) (x).begin(), (x).end()
#define bitcount(n) __builtin_popcountl((lint)(n))
#define fcout cout << fixed << setprecision(15)
#define highest(x) (63 - __builtin_clzl(x))
#define rep(i, n) for(int i = 0; i < int(n); i++)
#define rep2(i, l, r) for(int i = int(l); i < int(r); i++)
#define repr(i, n) for(int i = int(n) - 1; i >= 0; i--)
#define repr2(i, l, r) for(int i = int(r) - 1; i >= int(l); i--)
#define SZ(x) int(x.size())
constexpr int inf9 = 1e9; constexpr lint inf18 = 1e18;
inline void YES(bool condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
inline void Yes(bool condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
inline void assertNO(bool condition){ if(!condition){ cout << "NO" << endl; exit(0); } }
inline void assertNo(bool condition){ if(!condition){ cout << "No" << endl; exit(0); } }
inline void assertm1(bool condition){ if(!condition){ cout << -1 << endl; exit(0); } }
lint power(lint base, lint exponent, lint module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ lint root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }}
struct position{ int y, x; }; position mv[4] = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); }
template<class T, class U> string to_string(pair<T, U> x){ return to_string(x.first) + "," + to_string(x.second); } string to_string(string x){ return x; }
template<class T> string to_string(complex<T> x){ return to_string(make_pair(x.real(), x.imag())); }
template<class itr> void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++) cout << (i == start ? "" : " ") << (*i); if(!ans.empty()) ans.pop_back(); cout << ans << endl; }
template<class itr> void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } }
template<class T> T gcd(T a, T b){ if(b) return gcd(b, a % b); else return a; }
template<class T> T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct combination{ vector<lint> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } lint P(int n, int r){ if(r < 0 || n < r) return 0; return (fact[n] * inv[n - r] % mod); } lint C(int p, int q){ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };
template<class itr> bool next_sequence(itr first, itr last, int max_bound){ itr now = last; while(now != first){ now--; (*now)++; if((*now) == max_bound){ (*now) = 0; }else{ return true; } } return false; }
template<class itr, class itr2> bool next_sequence2(itr first, itr last, itr2 first2, itr2 last2){ itr now = last; itr2 now2 = last2; while(now != first){ now--, now2--; (*now)++; if((*now) == (*now2)){ (*now) = 0; }else{ return true; } } return false; }
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; }
inline int at(lint i, int j){ return (i >> j) & 1; }
random_device rnd;
bool is_in_board(lint y, lint x, lint H, lint W){ return (0 <= y && y < H && 0 <= x && x < W); }

const int sz = 350;
lint dp[sz][sz]; // 1を使った個数、1を移動した回数

int main(){
    string str;
    int K;
    cin >> str >> K;
    
    /*rep(i, 300){
        str.push_back('0' + i % 2);
    }
    K = 300;*/
    
    K = min(K, 300);
    vector<int> one_cnt{0};
    for(auto i: str){
        if(i == '0'){
            one_cnt.push_back(0);
        }else{
            one_cnt.back()++;
        }
    }
    vector<int> sum;
    int now_sum = 0;
    for(int i: one_cnt){
        now_sum += i;
        sum.push_back(now_sum);
    }
    int N = SZ(one_cnt), S = now_sum;
    rep(i, sz){
        rep(j, sz){
            dp[i][j] = 0;
        }
    }
    rep(i, K + 1){
        dp[S][i] = 1;
    }
    repr(now, N){
        //cout << now << endl;
        lint dp_sum_tate[sz + 1][sz + 1], dp_sum_naname[sz + 1][sz + 1];
        rep(i, sz + 1){
            rep(j, sz + 1){
                dp_sum_tate[i][j] = 0;
                dp_sum_naname[i][j] = 0;
            }
        }
        rep(i, sz){
            rep(j, sz){
                dp_sum_tate[i + 1][j] = dp[i][j];
                dp_sum_naname[i + 1][j + 1] = dp[i][j];
            }
        }
        rep(i, sz){
            rep(j, sz){
                dp_sum_tate[i + 1][j] += dp_sum_tate[i][j];
                dp_sum_tate[i + 1][j] %= mod;
            }
        }
        rep(i, sz){
            rep(j, sz){
                dp_sum_naname[i + 1][j + 1] += dp_sum_naname[i][j];
                dp_sum_naname[i + 1][j + 1] %= mod;
            }
        }
        vector<vector<lint>> dp2(S + 1, vector<lint>(K + 1));
        //vector<vector<lint>> dp3(S + 1, vector<lint>(K + 1));
        rep(used, S + 1){
            rep(changed, K + 1){
                dp2[used][changed] = 0;
                int l = max(0, sum[now] - used), m = one_cnt[now], r = one_cnt[now] + K - changed;
                l = min(l, 320 - used);
                m = min(m, 320 - used);
                /*rep2(i, l, m){
                    dp3[used][changed] += dp[used + i][changed];
                }
                rep2(i, max(l, m), r + 1){
                    dp3[used][changed] += dp[used + i][changed + i - m];
                }*/
                if(l < m){
                    dp2[used][changed] += (dp_sum_tate[used + m][changed] - dp_sum_tate[used + l][changed] + mod) % mod;
                }
                int lm = max(l, m);
                lm = min(lm, 320 - max(used, changed - m));
                r = min(r, 319 - max(used, changed - m));
                if(lm < r + 1){
                    dp2[used][changed] += dp_sum_naname[used + r + 1][changed + r + 1 - m] + mod;
                    dp2[used][changed] -= dp_sum_naname[used + lm][changed + lm - m];
                }
                
                dp2[used][changed] %= mod;
            }
        }
        /*cout << now << ": " << endl;
        rep(i, 10){
            array_output(dp[i], dp[i] + 10);
        }
        cout << endl;
        rep(i, 10){
            array_output(dp_sum_tate[i], dp_sum_tate[i] + 10);
        }
        cout << endl;
        rep(i, 10){
            array_output(dp_sum_naname[i], dp_sum_naname[i] + 10);
        }
        cout << endl;*/
        
        rep(i, S + 1){
            rep(j, K + 1){
                dp[i][j] = dp2[i][j];
            }
        }
    }
    cout << dp[0][0] << endl;
}






Measured memory_bytes: 6796