#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(x) (x).begin(),(x).end()
//#pragma GCC optimize ("-O3")
using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); }
typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60;
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<int MOD> struct ModInt {
    static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
    ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    int get() const { return (int)x; }
    ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
    ModInt &operator/=(ModInt that) { return *this *= that.inverse(); }
    ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
    ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
    ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
    ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
    ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0;
        while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
        return ModInt(u); }
    bool operator==(ModInt that) const { return x == that.x; }
    bool operator!=(ModInt that) const { return x != that.x; }
    ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; };
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
    ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; }
typedef ModInt<998244353> mint;
vector<string> split(string str, string delim) { // strをdelimそれぞれで分割
	vector<string> items;
	size_t dlm_idx;
	if (str.npos == (dlm_idx = str.find_first_of(delim))) {
		items.push_back(str.substr(0, dlm_idx));
	}
	while (str.npos != (dlm_idx = str.find_first_of(delim))) {
		if (str.npos == str.find_first_not_of(delim)) {
			break;
		}
		items.push_back(str.substr(0, dlm_idx));
		dlm_idx++;
		str = str.erase(0, dlm_idx);
		if (str.npos == str.find_first_of(delim) && "" != str) {
			items.push_back(str);
			break;
		}
	}
	return items;
}
/*---------------------------------------------------------------------------------------------------
　　　　　　　　　　　 ∧＿∧
　　　　　 ∧＿∧ 　（´<_｀ ）　 Welcome to My Coding Space!
　　　　 （ ´_ゝ`）　/　 ⌒i     @hamayanhamayan0
　　　　／　　　＼　 　  |　|
　　　 /　　 /￣￣￣￣/　　|
　 ＿_(__ﾆつ/　    ＿/ .| .|＿＿＿＿
　 　　　＼/＿＿＿＿/　（u　⊃
---------------------------------------------------------------------------------------------------*/














string S; int K;
int N;
int A[303];
mint dp[603][603];
mint imos1[603][603], imos2[603][603];
//---------------------------------------------------------------------------------------------------
void _main() {
    cin >> S >> K;
    N = S.length();
    chmin(K, N);

    auto v = split(S, "0");
    int M = v.size();
    rep(i, 0, M) A[i] = v[i].length();
    
    dp[0][0] = 1;
    rep(i, 0, M) {
        rep(need, 0, N) rep(k, 0, K + 1) imos1[need][k] = 0;
        rep(need, 0, N) rep(k, 0, K + 1) imos2[need][k] = 0;

        /*
                   rep(a2, 0, A[i] + 1) if (0 <= need - (A[i] - a2)) dp[ne][need - (A[i] - a2)][k + (A[i] - a2)] += dp[cu][need][k];
            rep(a2, A[i] + 1, N + 1) dp[ne][need + (a2 - A[i])][k] += dp[cu][need][k];
  
        */

        rep(need, 0, N) rep(k, 0, K + 1) {
            int L = min(need, A[i]);
            int R = 0;

            imos1[need - L][k + L] += dp[need][k];
            if(k) imos1[need + 1][k - 1] -= dp[need][k];

            imos2[need + 1][k] += dp[need][k];
        }

        rep(need, 1, N) rrep(k, K - 1, 0) imos1[need][k] += imos1[need - 1][k + 1];
        rep(need, 1, N) rep(k, 0, K + 1) imos2[need][k] += imos2[need - 1][k];
        rep(need, 0, N) rep(k, 0, K + 1) dp[need][k] = imos1[need][k] + imos2[need][k];
    }

    mint ans = 0;
    rep(k, 0, K + 1) ans += dp[0][k];
    cout << ans << endl;
}







Measured memory_bytes: 7868