#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt(): val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) const {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }
  ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }
  ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }
  ModInt &operator/=(const ModInt &x) {
    // assert(__gcd(static_cast<int>(x.val), mod) == 1);
    unsigned a = x.val, b = mod; int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() { if (++val == mod) val = 0; return *this; }
  ModInt operator++(int) { ModInt res = *this; ++*this; return res; }
  ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }
  ModInt operator--(int) { ModInt res = *this; --*this; return res; }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }
  friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0) return ModInt(0);
    return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
  }
};

int main() {
  string s; int K; cin >> s >> K;
  while (!s.empty() && s.back() == '0') s.pop_back();
  reverse(ALL(s));
  while (!s.empty() && s.back() == '1') s.pop_back();
  reverse(ALL(s));
  vector<int> a;
  for (int i = 1; i < s.length();) {
    if (s[i] == '0') {
      a.emplace_back(0);
      ++i;
      continue;
    }
    int j = i + 1;
    while (j < s.length() && s[j] == '1') ++j;
    a.emplace_back(j - i);
    i = j + 1;
  }
  a.emplace(a.begin(), 0);
  int n = a.size(), m = count(ALL(s), '1');
  int prev = 0;
  vector dp(2, vector(m + 1, vector(m + 1, vector(2, ModInt(0)))));
  dp[0][0][0][0] = 1;
  REP(i, n + 1) {
    if (i > 0) {
      REP(j, m + 1) FOR(k, j + 1, m + 1) dp[i & 1][j][k][0] += dp[i & 1][j][k - 1][0];
      REP(k, m + 1) FOR(j, 1, k + 1) dp[i & 1][j][k][1] += dp[i & 1][j - 1][k][1];
    }
    if (i < n) {
      REP(j, m + 1) FOR(k, j, m + 1) {
        int used = prev + k - j;
        ModInt cur = dp[i & 1][j][k][0] + dp[i & 1][j][k][1];
        if (used + a[i] < m) {
          if (k + 1 <= m) {
            dp[(i + 1) & 1][j][k + 1][0] += cur;
            if (k + m - (used + a[i]) + 1 <= m) dp[(i + 1) & 1][j][k + m - (used + a[i]) + 1][0] -= cur;
          }
        }
        if (j + max(used + a[i] - m, 0) <= k) {
          dp[(i + 1) & 1][j + max(used + a[i] - m, 0)][k][1] += cur;
          if (j + a[i] + 1 <= k) dp[(i + 1) & 1][j + a[i] + 1][k][1] -= cur;
        }
      }
      // REP(j, m + 1) REP(k, m + 1) cout << dp[i & 1][j][k][0] + dp[i & 1][j][k][1] << " \n"[k == m];
      // cout << '\n';
      REP(j, m + 1) REP(k, m + 1) {
        dp[i & 1][j][k][0] = dp[i & 1][j][k][1] = 0;
      }
      prev += a[i];
    }
  }
  ModInt ans = 0;
  for (int j = 0; j <= K && j <= m; ++j) {
    ans += dp[n & 1][j][j][0] + dp[n & 1][j][j][1];
  }
  cout << ans << '\n';
  return 0;
}


Measured memory_bytes: 16648