#include <bits/stdc++.h>
// #include <atcoder/all>
using namespace std;
// using namespace atcoder;
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
#ifdef __LOCAL
#define debug(x) cerr << __LINE__ << ": " << #x << " = " << (x) << '\n'
#define debugArray(x, n)                                      \
  cerr << __LINE__ << ": " << #x << " = {";                   \
  for (long long hoge = 0; (hoge) < (long long)(n); ++(hoge)) \
    cerr << ((hoge) ? "," : "") << x[hoge];                   \
  cerr << "}" << '\n'
#define debugMatrix(x, h, w)                                         \
  cerr << __LINE__ << ": " << #x << " =\n";                          \
  for (long long hoge = 0; (hoge) < (long long)(h); ++(hoge)) {      \
    cerr << ((hoge ? " {" : "{{"));                                  \
    for (long long fuga = 0; (fuga) < (long long)(w); ++(fuga))      \
      cerr << ((fuga ? ", " : "")) << x[hoge][fuga];                 \
    cerr << "}" << (hoge + 1 == (long long)(h) ? "}" : ",") << '\n'; \
  }
#else
#define debug(x) (void(0))
#define debugArray(x, n) (void(0))
#define debugMatrix(x, h, w) (void(0))
#endif

template <int mod>
struct ModInt {
  int64_t x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod)) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) { return *this *= p.inverse(); }
  ModInt operator-() const { return ModInt() - *this; }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b) t = a / b, swap(a -= t * b, b), swap(u -= t * v, v);
    return ModInt(u);
  }
  ModInt pow(int64_t e) const {
    ModInt ret(1);
    for (ModInt b = *this; e; e >>= 1, b *= b)
      if (e & 1) ret *= b;
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int modulo() { return mod; }
  int get() const { return x; }
};

template <typename T>
struct BinaryIndexedTree {
  vector<T> dat;
  BinaryIndexedTree(int n) : dat(n + 1, 0) {}
  BinaryIndexedTree(int n, T a) : BinaryIndexedTree(vector<T>(n, a)) {}
  BinaryIndexedTree(vector<T> y) : dat(y.size() + 1, 0) {
    for (size_t i = 0; i < y.size(); ++i) dat[i + 1] = y[i];
    for (int i = 1; i < (int)dat.size(); ++i)
      if (i + (i & -i) < (int)dat.size()) dat[i + (i & -i)] += dat[i];
  }
  void add(int i, T a = 1) {
    for (++i; i < (int)dat.size(); i += i & -i) dat[i] += a;
  }
  T sum(int i) {  // sum [0,i)
    T s = 0;
    for (; i > 0; i &= i - 1) s += dat[i];
    return s;
  }
  // sum [l,r)
  T sum(int l, int r) { return sum(r) - sum(l); }
  T operator[](size_t k) { return sum(k + 1) - sum(k); }
  // min { i : sum(i+1) > k } -> kth element(0-indexed)
  int find(T k) const {
    int i = 0;
    for (int p = 1 << (__lg(dat.size() - 1) + 1); p > 0; p >>= 1)
      if (i + p < (int)dat.size() && dat[i + p] <= k) k -= dat[i += p];
    return i + 1 == (int)dat.size() ? -1 : i;  // -1 -> no solutions
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  using Mint = ModInt<998244353>;
  int N, K;
  cin >> N >> K;
  int p[N];
  for (int i = 0; i < N; i++) {
    cin >> p[i];
    p[i]--;
  }
  BinaryIndexedTree<Mint> bit1(N), bit2(N);
  Mint ans = 0;
  Mint P = Mint(K - 1) / Mint(K);
  for (int i = 0; i < N; i++) {
    int f = max(0, i - (K - 1));
    Mint tmp = P.pow(f);
    ans += bit2.sum(p[i], N) - bit1.sum(p[i], N) * tmp / 2
           + bit1.sum(0, p[i]) * tmp / 2;
    bit1.add(p[i], tmp.inverse());
    bit2.add(p[i], 1);
  }
  cout << ans << '\n';
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

Given are a permutation p_1, p_2, \dots, p_N of (1, 2, ..., N) and an integer K. Maroon performs the following operation for i = 1, 2, \dots, N - K + 1 in this order:

* Shuffle p_i, p_{i + 1}, \dots, p_{i + K - 1} uniformly randomly.



Find the expected value of the inversion number of the sequence after all the operations are performed, and print it modulo 998244353.

More specifically, from the constraints of this problem, it can be proved that the expected value is always a rational number, which can be represented as an irreducible fraction \frac{P}{Q}, and that the integer R that satisfies R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353 is uniquely determined. Print this R.

Here, the inversion number of a sequence a_1, a_2, \dots, a_N is defined to be the number of ordered pairs (i, j) that satisfy i < j, a_i > a_j.

Constraints

* 2 \leq N \leq 200,000
* 2 \leq K \leq N
* (p_1, p_2, \dots, p_N) is a permutation of (1, 2, \dots, N).
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
p_1 p_2 ... p_N


Output

Print the expected value modulo 998244353.

Examples

Input

3 2
1 2 3


Output

1


Input

10 3
1 8 4 9 2 3 7 10 5 6


Output

164091855

### Response

```cpp
#include <bits/stdc++.h>
// #include <atcoder/all>
using namespace std;
// using namespace atcoder;
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
#ifdef __LOCAL
#define debug(x) cerr << __LINE__ << ": " << #x << " = " << (x) << '\n'
#define debugArray(x, n)                                      \
  cerr << __LINE__ << ": " << #x << " = {";                   \
  for (long long hoge = 0; (hoge) < (long long)(n); ++(hoge)) \
    cerr << ((hoge) ? "," : "") << x[hoge];                   \
  cerr << "}" << '\n'
#define debugMatrix(x, h, w)                                         \
  cerr << __LINE__ << ": " << #x << " =\n";                          \
  for (long long hoge = 0; (hoge) < (long long)(h); ++(hoge)) {      \
    cerr << ((hoge ? " {" : "{{"));                                  \
    for (long long fuga = 0; (fuga) < (long long)(w); ++(fuga))      \
      cerr << ((fuga ? ", " : "")) << x[hoge][fuga];                 \
    cerr << "}" << (hoge + 1 == (long long)(h) ? "}" : ",") << '\n'; \
  }
#else
#define debug(x) (void(0))
#define debugArray(x, n) (void(0))
#define debugMatrix(x, h, w) (void(0))
#endif

template <int mod>
struct ModInt {
  int64_t x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod)) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) { return *this *= p.inverse(); }
  ModInt operator-() const { return ModInt() - *this; }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b) t = a / b, swap(a -= t * b, b), swap(u -= t * v, v);
    return ModInt(u);
  }
  ModInt pow(int64_t e) const {
    ModInt ret(1);
    for (ModInt b = *this; e; e >>= 1, b *= b)
      if (e & 1) ret *= b;
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int modulo() { return mod; }
  int get() const { return x; }
};

template <typename T>
struct BinaryIndexedTree {
  vector<T> dat;
  BinaryIndexedTree(int n) : dat(n + 1, 0) {}
  BinaryIndexedTree(int n, T a) : BinaryIndexedTree(vector<T>(n, a)) {}
  BinaryIndexedTree(vector<T> y) : dat(y.size() + 1, 0) {
    for (size_t i = 0; i < y.size(); ++i) dat[i + 1] = y[i];
    for (int i = 1; i < (int)dat.size(); ++i)
      if (i + (i & -i) < (int)dat.size()) dat[i + (i & -i)] += dat[i];
  }
  void add(int i, T a = 1) {
    for (++i; i < (int)dat.size(); i += i & -i) dat[i] += a;
  }
  T sum(int i) {  // sum [0,i)
    T s = 0;
    for (; i > 0; i &= i - 1) s += dat[i];
    return s;
  }
  // sum [l,r)
  T sum(int l, int r) { return sum(r) - sum(l); }
  T operator[](size_t k) { return sum(k + 1) - sum(k); }
  // min { i : sum(i+1) > k } -> kth element(0-indexed)
  int find(T k) const {
    int i = 0;
    for (int p = 1 << (__lg(dat.size() - 1) + 1); p > 0; p >>= 1)
      if (i + p < (int)dat.size() && dat[i + p] <= k) k -= dat[i += p];
    return i + 1 == (int)dat.size() ? -1 : i;  // -1 -> no solutions
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  using Mint = ModInt<998244353>;
  int N, K;
  cin >> N >> K;
  int p[N];
  for (int i = 0; i < N; i++) {
    cin >> p[i];
    p[i]--;
  }
  BinaryIndexedTree<Mint> bit1(N), bit2(N);
  Mint ans = 0;
  Mint P = Mint(K - 1) / Mint(K);
  for (int i = 0; i < N; i++) {
    int f = max(0, i - (K - 1));
    Mint tmp = P.pow(f);
    ans += bit2.sum(p[i], N) - bit1.sum(p[i], N) * tmp / 2
           + bit1.sum(0, p[i]) * tmp / 2;
    bit1.add(p[i], tmp.inverse());
    bit2.add(p[i], 1);
  }
  cout << ans << '\n';
  return 0;
}

```