#include <bits/stdc++.h>
#define ADD(a, b) a = (a + ll(b)) % mod
#define MUL(a, b) a = (a * ll(b)) % mod
#define MAX(a, b) a = max(a, b)
#define MIN(a, b) a = min(a, b)
#define rep(i, a, b) for(int i = int(a); i < int(b); i++)
#define rer(i, a, b) for(int i = int(a) - 1; i >= int(b); i--)
#define all(a) (a).begin(), (a).end()
#define sz(v) (int)(v).size()
#define pb push_back
#define sec second
#define fst first
#define debug(fmt, ...) Debug(__LINE__, ":", fmt, ##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<int, pi> ppi;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> mat;
typedef complex<double> comp;
void Debug() {cerr << '\n'; }
template<class FIRST, class... REST>void Debug(FIRST arg, REST... rest){
	cerr<<arg<<" ";Debug(rest...);}
template<class T>ostream& operator<<(ostream& out,const vector<T>& v) {
	out<<"[";if(!v.empty()){rep(i,0,sz(v)-1)out<<v[i]<<", ";out<<v.back();}out<<"]";return out;}
template<class S, class T>ostream& operator<<(ostream& out,const pair<S, T>& v){
	out<<"("<<v.first<<", "<<v.second<<")";return out;}
const int MAX_N = 500010;
const int MAX_V = 100010;
const double eps = 1e-6;
const ll mod = 998244353;
const int inf = (1 << 30) - 1;
const ll linf = 1LL << 60;
const double PI = 3.14159265358979323846;
mt19937 rng; //use it by rng() % mod, shuffle(all(vec), rng)
///////////////////////////////////////////////////////////////////////////////////////////////////

string S;
int K, N;
int A[MAX_N];
int D[MAX_N];

ll dp[2][620][620];
ll ep[620][620];

void solve() {
	cin >> S;
	cin >> K;
	N = sz(S);
	int M = 0;
	rep(i, 0, N) {
		if(S[i] == '0') M++;
		else A[M]++;
	}
	M += 1;
	// debug(vi(A, A + M));
	rep(i, 0, M) {
		D[i + 1] = D[i] + A[i];
	}
	N = accumulate(A, A + N, 0);
	int now = 0, nex = 1;
	dp[0][0][0] = 1;
	rep(i, 0, M) {
		memset(dp[nex], 0, sizeof(dp[nex]));
		memset(ep, 0, sizeof(ep));
		// put less then A[i]
		rep(j, 0, N + 1) { //how many put
			if(j < D[i]) continue;
			rep(k, 0, N + 1) { //diff
				ADD(dp[nex][j + A[i]][k + A[i]], mod - dp[now][j][k]);
				ADD(dp[nex][j][k], dp[now][j][k]);
			}
		}
		rep(j, 0, N + 1) {
			rep(k, 0, 610) {
				if(j + k <= 610) {
					ADD(dp[nex][j + 1][k + 1], dp[nex][j][k]);
				}
				else break;
			}
		}
		// debug("omo");
		// rep(j, 0, N + 1) {
		// 	rep(k, 0, N + 1) {
		// 		debug(i, j, k, dp[nex][j][k]);
		// 	}
		// }
		// debug("omoend");
		//else
		rep(j, 0, N + 1) {
			rep(k, 0, N + 1) {
				if(j + A[i] <= N && j >= D[i]) {
					ADD(ep[j + A[i]][k + A[i]], dp[now][j][k]);
					ADD(ep[N + 1][k + A[i]], mod - dp[now][j][k]);
				}
			}
		}
		rep(k, 0, N + 1) {
			rep(j, 0, N + 1) {
				ADD(ep[j + 1][k], ep[j][k]);
			}
		}
		rep(k, 0, N + 1) {
			rep(j, 0, N + 1) {
				ADD(dp[nex][j][k], ep[j][k]);
			}
		}
		// debug("yes");
		// rep(j, 0, N + 1) {
		// 	rep(k, 0, N + 1) {
		// 		debug(i, j, k, dp[nex][j][k]);
		// 	}
		// }
		// debug("yesend");
		
		swap(now, nex);
	}
	ll res = 0;
	rep(i, 0, N + 1) {
		int dif = N - i;
		if(dif <= K) ADD(res, dp[now][N][i]);
	}
	cout << res << "\n";
}

uint32_t rd() {
	uint32_t res;
#ifdef __MINGW32__
	asm volatile("rdrand %0" :"=a"(res) ::"cc");
#else
	res = std::random_device()();
#endif
	return res;
}

int main() {
#ifndef LOCAL
	ios::sync_with_stdio(false);
    cin.tie(0);
#endif
    cout << fixed;
	cout.precision(20);
    cerr << fixed;
	cerr.precision(6);
	rng.seed(rd());
#ifdef LOCAL
	//freopen("in.txt", "wt", stdout); //for tester
	if(!freopen("in.txt", "rt", stdin)) return 1;
#endif	
	solve();
    cerr << "Time: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
	return 0;
}




Measured memory_bytes: 12876