#include <bits/stdc++.h>
 
using namespace std;
 
#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl;
#define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;}
typedef long long ll;
#define int ll
 
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(int)(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
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 (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
#define Sp(p) cout<<setprecision(25)<< fixed<<p<<endl;
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {1, 0, -1, 0}, dy = {0, 1, 0, -1};
vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'


const int MAXN = 555555;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
  if (p < 0) {
	x = mod_pow(x, M - 2, M);
	p = -p;
  }
  ll a = 1;
  while (p) {
	if (p % 2)
	  a = a*x%M;
	x = x*x%M;
	p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) {
  return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
  fact[0] = fact[1] = rfact[0] = rfact[1] = 1;
  for (ll i = 2; i <= n; i++) {
	fact[i] = i * fact[i - 1] % M;
	// rfact[i] = mod_inverse(fact[i], M);
  }
}

//http://drken1215.hatenablog.com/entry/2018/06/08/210000
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ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n) return 0;
  assert(fact[2] == 2);
  ll ret = fact[n];
  if (rfact[r] == 0) {
	rfact[r] = mod_inverse(fact[r], M);
  }
  ret = (ret*rfact[r]) % M;
  if (rfact[n - r] == 0) {
	rfact[n - r] = mod_inverse(fact[n - r], M);
  }
  ret = (ret*rfact[n - r]) % M;
  return ret;
}

ll nHr(ll n, ll r) {
  return nCr(n+r-1, r);
}

struct dice {
  mt19937 mt;
  dice() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
  // [0, x)の一様乱数
  ll operator()(ll x) { return this->operator()(0, x); }
  // [x, y)の一様乱数
  ll operator()(ll x, ll y) {
	uniform_int_distribution<ll> dist(x, y - 1);
	return dist(mt);
  }
  vl operator()(int n, ll x, ll y) {
	vl res(n);
	for (int i = 0; i < n; i++) res[i] = this->operator()(x, y);
	return res;
  }
} rnd;

signed main() {
	fio();
	
	int N = 300;
	string s(N, '?');
	// rep (i, N) {
	// 	s[i] = '0' + rnd(2);
	// }
	// DEBUG(s);
	cin >> s;
	ll k = 1000000;
	cin >> k;


	while (s.size() > 0 and s.back() == '0') s.pop_back();
	while (s.size() > 0 and s[0] == '1') s.erase(s.begin());
	int n = s.size();

	bool ze = false, on = false;
	rep (i, n) {
		if (s[i] == '0') ze = true;
		if (s[i] == '1') on = true;
	}
	if (not ze or not on) {
		cout << 1 << endl;
		return 0;
	}

	int num = 0;
	vi a;
	rep (i, n) {
		if (s[i] == '0') {
			a.push_back(num);
			num = 0;
		}
		else {
			num++;
		}
	}
	a.push_back(num);
	// DEBUG_VEC(a);

	int m = a.size();
	k = min(k, 400LL);
	vector<vll> dp(m + 1, vll(k + 1, vl(k + 1)));
	dp[0][0][0] = 1;

	rep (i, m) {
		rep (j, k + 1) {
			rep (l, k + 1) {
				if (dp[i][j][l] == 0) continue;
				// 変化なし
				(dp[i + 1][j][l] += dp[i][j][l]) %= MOD;
				// 増やす
				for (int add = 1; l + add <= k and j + add <= k; add++) {
					(dp[i + 1][j + add][l + add] += dp[i][j][l]) %= MOD;
				}
				// 減らす
				for (int del = 1; del <= a[i] and l - del >= 0; del++) {
					(dp[i + 1][j][l - del] += dp[i][j][l]) %= MOD;
				}
			}
		}
	}

	ll ans = 0;
	rep (i, k + 1) {
		ans += dp[m][i][0];
	}
	ans %= MOD;
	cout << ans << endl;
}

Measured memory_bytes: 205996