#include <bits/stdc++.h>
using namespace std;

template <int MOD_> struct modnum {
	static constexpr int MOD = MOD_;
	static_assert(MOD_ > 0, "MOD must be positive");

private:
	using ll = long long;

	int v;

	static int minv(int a, int m) {
		a %= m;
		assert(a);
		return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a);
	}

public:

	modnum() : v(0) {}
	modnum(ll v_) : v(int(v_ % MOD)) { if (v < 0) v += MOD; }
	explicit operator int() const { return v; }
	friend std::ostream& operator << (std::ostream& out, const modnum& n) { return out << int(n); }
	friend std::istream& operator >> (std::istream& in, modnum& n) { ll v_; in >> v_; n = modnum(v_); return in; }

	friend bool operator == (const modnum& a, const modnum& b) { return a.v == b.v; }
	friend bool operator != (const modnum& a, const modnum& b) { return a.v != b.v; }

	modnum inv() const {
		modnum res;
		res.v = minv(v, MOD);
		return res;
	}
	friend modnum inv(const modnum& m) { return m.inv(); }
	modnum neg() const {
		modnum res;
		res.v = v ? MOD-v : 0;
		return res;
	}
	friend modnum neg(const modnum& m) { return m.neg(); }

	modnum operator- () const {
		return neg();
	}
	modnum operator+ () const {
		return modnum(*this);
	}

	modnum& operator ++ () {
		v ++;
		if (v == MOD) v = 0;
		return *this;
	}
	modnum& operator -- () {
		if (v == 0) v = MOD;
		v --;
		return *this;
	}
	modnum& operator += (const modnum& o) {
		v += o.v;
		if (v >= MOD) v -= MOD;
		return *this;
	}
	modnum& operator -= (const modnum& o) {
		v -= o.v;
		if (v < 0) v += MOD;
		return *this;
	}
	modnum& operator *= (const modnum& o) {
		v = int(ll(v) * ll(o.v) % MOD);
		return *this;
	}
	modnum& operator /= (const modnum& o) {
		return *this *= o.inv();
	}

	friend modnum operator ++ (modnum& a, int) { modnum r = a; ++a; return r; }
	friend modnum operator -- (modnum& a, int) { modnum r = a; --a; return r; }
	friend modnum operator + (const modnum& a, const modnum& b) { return modnum(a) += b; }
	friend modnum operator - (const modnum& a, const modnum& b) { return modnum(a) -= b; }
	friend modnum operator * (const modnum& a, const modnum& b) { return modnum(a) *= b; }
	friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= b; }
};

template <typename T> T pow(T a, long long b) {
	assert(b >= 0);
	T r = 1; while (b) { if (b & 1) r *= a; b >>= 1; a *= a; } return r;
}

using num = modnum<998244353>;

vector<num> fact, ifact;

void init(){
	int N = 1100000;
	fact = {1};
	for(int i = 1; i < N; i++) fact.push_back(i * fact[i-1]);
	ifact.resize(N);
	ifact.back() = 1 / fact.back();
	for(int i = N - 1; i > 0; i--) ifact[i-1] = i * ifact[i];
}

num ncr(int n, int k){
	if(k < 0 || k > n) return 0;
	return fact[n] * ifact[k] * ifact[n-k];
}

int main(){
	ios_base::sync_with_stdio(false), cin.tie(nullptr);
	init();

	string s;
	int k;
	cin >> s >> k;
	s += "0";
	vector<int> cnt;
	int cur = 0;
	int ntot = 0;
	for(char c : s){
		if(c == '1'){
			cur++;
			ntot++;
		}
		if(c == '0'){
			cnt.push_back(cur);
			cur = 0;
		}
	}
	k = min(k, 400);
	vector<vector<num> > dp(ntot + 1, vector<num>(k+1, 0));
	dp[0][0] = 1;
	int ctot = 0;
	for(int c : cnt){
		ctot += c;
		vector<vector<num> > z(ntot + 1, vector<num>(k+1, 0));
		for(int a = 0; a <= ntot; a++){
			for(int b = 0; b <= k; b++){
				for(int na = 0; a + na <= ntot; na++){
					if(a + na < ctot) continue;
					int nb = b + max(na - c, 0);
					if(nb > k) continue;
					z[a + na][nb] += dp[a][b];
				}
			}
		}
		dp = z;
	}
	num ans = 0;
	for(int i = 0; i <= k; i++) ans += dp[ntot][i];
	cout << ans << '\n';
}

Measured memory_bytes: 12840