description: You are given a binary string (i. e. a string consisting of characters 0 and/or 1) s of length n. You can perform the following operation with the string s at most once: choose a substring (a contiguous subsequence) of s having exactly k characters 1 in it, and shuffle it (reorder the characters in the substring as you wish).
  
  Calculate the number of different strings which can be obtained from s by performing this operation at most once.
  
  Input
  
  The first line contains two integers n and k (2 ≤ n ≤ 5000; 0 ≤ k ≤ n).
  
  The second line contains the string s of length n, consisting of characters 0 and/or 1.
  
  Output
  
  Print one integer — the number of different strings which can be obtained from s by performing the described operation at most once. Since the answer can be large, output it modulo 998244353.
  
  Examples
  
  Input
  
  
  7 2
  1100110
  
  
  Output
  
  
  16
  
  
  Input
  
  
  5 0
  10010
  
  
  Output
  
  
  1
  
  
  Input
  
  
  8 1
  10001000
  
  
  Output
  
  
  10
  
  
  Input
  
  
  10 8
  0010011000
  
  
  Output
  
  
  1
  
  Note
  
  Some strings you can obtain in the first example:
  
    * to obtain 0110110, you can take the substring from the 1-st character to the 4-th character, which is 1100, and reorder its characters to get 0110; 
    * to obtain 1111000, you can take the substring from the 3-rd character to the 7-th character, which is 00110, and reorder its characters to get 11000; 
    * to obtain 1100101, you can take the substring from the 5-th character to the 7-th character, which is 110, and reorder its characters to get 101. 
  
  
  
  In the second example, k = 0 so you can only choose the substrings consisting only of 0 characters. Reordering them doesn't change the string at all, so the only string you can obtain is 10010.
solution: #include <bits/stdc++.h>
  using namespace std;
  template <typename T>
  T inverse(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
      T t = m / a;
      m -= t * a;
      swap(a, m);
      u -= t * v;
      swap(u, v);
    }
    assert(m == 1);
    return u;
  }
  template <typename T>
  class Modular {
   public:
    using Type = typename decay<decltype(T::value)>::type;
    constexpr Modular() : value() {}
    template <typename U>
    Modular(const U &x) {
      value = normalize(x);
    }
    template <typename U>
    static Type normalize(const U &x) {
      Type v;
      if (-mod() <= x && x < mod())
        v = static_cast<Type>(x);
      else
        v = static_cast<Type>(x % mod());
      if (v < 0) v += mod();
      return v;
    }
    const Type &operator()() const { return value; }
    template <typename U>
    explicit operator U() const {
      return static_cast<U>(value);
    }
    constexpr static Type mod() { return T::value; }
    Modular &operator+=(const Modular &other) {
      if ((value += other.value) >= mod()) value -= mod();
      return *this;
    }
    Modular &operator-=(const Modular &other) {
      if ((value -= other.value) < 0) value += mod();
      return *this;
    }
    template <typename U>
    Modular &operator+=(const U &other) {
      return *this += Modular(other);
    }
    template <typename U>
    Modular &operator-=(const U &other) {
      return *this -= Modular(other);
    }
    Modular &operator++() { return *this += 1; }
    Modular &operator--() { return *this -= 1; }
    Modular operator++(int) {
      Modular result(*this);
      *this += 1;
      return result;
    }
    Modular operator--(int) {
      Modular result(*this);
      *this -= 1;
      return result;
    }
    Modular operator-() const { return Modular(-value); }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      value = normalize(static_cast<int64_t>(value) *
                        static_cast<int64_t>(rhs.value));
      return *this;
    }
    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, long long>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      long long q = static_cast<long long>(static_cast<long double>(value) *
                                           rhs.value / mod());
      value = normalize(value * rhs.value - q * mod());
      return *this;
    }
    template <typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
      value = normalize(value * rhs.value);
      return *this;
    }
    Modular &operator/=(const Modular &other) {
      return *this *= Modular(inverse(other.value, mod()));
    }
    friend const Type &abs(const Modular &x) { return x.value; }
    template <typename U>
    friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);
    template <typename U>
    friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);
    template <typename V, typename U>
    friend V &operator>>(V &stream, Modular<U> &number);
  
   private:
    Type value;
  };
  template <typename T>
  bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
    return lhs.value == rhs.value;
  }
  template <typename T, typename U>
  bool operator==(const Modular<T> &lhs, U rhs) {
    return lhs == Modular<T>(rhs);
  }
  template <typename T, typename U>
  bool operator==(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) == rhs;
  }
  template <typename T>
  bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
    return !(lhs == rhs);
  }
  template <typename T, typename U>
  bool operator!=(const Modular<T> &lhs, U rhs) {
    return !(lhs == rhs);
  }
  template <typename T, typename U>
  bool operator!=(U lhs, const Modular<T> &rhs) {
    return !(lhs == rhs);
  }
  template <typename T>
  bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
    return lhs.value < rhs.value;
  }
  template <typename T>
  Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T, typename U>
  Modular<T> operator+(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T, typename U>
  Modular<T> operator+(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) += rhs;
  }
  template <typename T>
  Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator-(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator-(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) -= rhs;
  }
  template <typename T>
  Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator*(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator*(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) *= rhs;
  }
  template <typename T>
  Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator/(const Modular<T> &lhs, U rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> operator/(U lhs, const Modular<T> &rhs) {
    return Modular<T>(lhs) /= rhs;
  }
  template <typename T, typename U>
  Modular<T> power(const Modular<T> &a, const U &b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
      if (p & 1) res *= x;
      x *= x;
      p >>= 1;
    }
    return res;
  }
  template <typename T>
  bool IsZero(const Modular<T> &number) {
    return number() == 0;
  }
  template <typename T>
  string to_string(const Modular<T> &number) {
    return to_string(number());
  }
  template <typename U, typename T>
  U &operator<<(U &stream, const Modular<T> &number) {
    return stream << number();
  }
  template <typename U, typename T>
  U &operator>>(U &stream, Modular<T> &number) {
    typename common_type<typename Modular<T>::Type, long long>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
  }
  constexpr int md = (int)998244353;
  using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
  vector<Mint> fact(1, 1);
  vector<Mint> inv_fact(1, 1);
  Mint C(int n, int k) {
    if (k < 0 || k > n) {
      return 0;
    }
    while ((int)fact.size() < n + 1) {
      fact.push_back(fact.back() * (int)fact.size());
      inv_fact.push_back(1 / fact.back());
    }
    return fact[n] * inv_fact[k] * inv_fact[n - k];
  }
  int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    vector<int> pos;
    for (int i = 0; i < n; i++) {
      if (s[i] == '1') pos.emplace_back(i);
    }
    if (k == 0 || k > pos.size()) {
      cout << 1;
      return 0;
    }
    int l = 0, r = pos[k - 1];
    int cnt0 = r - l + 1 - k, cnt1 = k;
    Mint q = C(5005, 1);
    Mint ans = fact[cnt0 + cnt1] / fact[cnt0] / fact[cnt1] - 1;
    r++;
    if (r < n) {
      if (s[r] == '0')
        cnt0++;
      else
        cnt1++;
    }
    while (r < n) {
      while (cnt1 > k) {
        if (s[l] == '0')
          cnt0--;
        else
          cnt1--;
        l++;
      }
      int c1 = cnt1, c0 = cnt0;
      if (s[r] == '1')
        c0--;
      else
        c1--;
      if (c0 >= 0 && c1 >= 0) ans += fact[c0 + c1] / fact[c0] / fact[c1];
      r++;
      if (r == n) break;
      if (s[r] == '0')
        cnt0++;
      else
        cnt1++;
    }
    cout << ans + 1;
    return 0;
  }
  