Problem: You are given a positive integer k and an array a_1, a_2, …, a_n of non-negative distinct integers not smaller than k and not greater than 2^c-1.

In each of the next k seconds, one element is chosen randomly equiprobably out of all n elements and decreased by 1.

For each integer x, 0 ≤ x ≤ 2^c - 1, you need to find the probability that in the end the bitwise XOR of all elements of the array is equal to x. 

Each of these values can be represented as an irreducible fraction p/q, and you need to find the value of p ⋅ q^{-1} modulo 998 244 353. 

Input

The first line of input contains three integers n, k, c (1 ≤ n ≤ (2^c - k), 1 ≤ k ≤ 16, 1 ≤ c ≤ 16).

The second line contains n distinct integers a_1, a_2, …, a_n (k ≤ a_i ≤ 2^c-1).

Output

Print 2^c integers: the probability that the bitwise XOR is equal to x in the end for x in \{0, 1, …, 2^c-1\} modulo 998 244 353.

Example

Input


4 1 3
1 2 3 4


Output


0 0 0 748683265 0 499122177 0 748683265 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;
void doReplace() {}
template <typename T, typename U, typename... Vs>
void doReplace(T& t, const U& u, Vs&&... vs) {
  t = u;
  doReplace(vs...);
}
template <typename T, typename... Us>
T minim(T& was, const T& cand, Us&&... us) {
  if (was > cand) {
    was = cand;
    doReplace(us...);
  }
  return was;
}
template <typename T, typename... Us>
T maxim(T& was, const T& cand, Us&&... us) {
  if (was < cand) {
    was = cand;
    doReplace(us...);
  }
  return was;
}
template <typename D>
D dPower(D base, ll exponent) {
  if (exponent < 0) {
    return dPower(1 / base, -exponent);
  }
  if (exponent == 0) {
    return 1;
  }
  if ((exponent & 1) == 1) {
    return dPower(base, exponent - 1) * base;
  } else {
    D res = dPower(base, exponent >> 1);
    return res * res;
  }
}
class NumberIterator : iterator<forward_iterator_tag, int> {
 public:
  int v;
  NumberIterator(int v) : v(v) {}
  operator int&() { return v; }
  int operator*() { return v; }
};
class range : pii {
 public:
  range(int begin, int end) : pii(begin, max(begin, end)) {}
  range(int n) : pii(0, max(0, n)) {}
  NumberIterator begin() { return first; }
  NumberIterator end() { return second; }
};
template <typename T>
class NeedFill {
  struct Fallback {
    int begin;
  };
  struct Derived : T, Fallback {};
  template <typename U, U>
  struct Check;
  typedef char Yes[1];
  typedef char No[2];
  template <typename U>
  static No& func(Check<int Fallback::*, &U::begin>*);
  template <typename U>
  static Yes& func(...);

 public:
  enum { value = sizeof(func<Derived>(0)) == sizeof(Yes) };
};
template <>
class NeedFill<int> {
 public:
  const static bool value = false;
};
template <>
class NeedFill<bool> {
 public:
  const static bool value = true;
};
template <>
class NeedFill<ll> {
 public:
  const static bool value = false;
};
template <>
class NeedFill<double> {
 public:
  const static bool value = false;
};
template <>
class NeedFill<ld> {
 public:
  const static bool value = false;
};
template <>
class NeedFill<char> {
 public:
  const static bool value = false;
};
template <typename T>
class arr {
  T* b;
  int n;
  void allocate(int sz) {
    n = sz;
    if (sz > 0) {
      b = (T*)(::operator new(sz * sizeof(T)));
    } else {
      b = nullptr;
    }
  }

 public:
  arr(int n = 0) {
    allocate(n);
    if (NeedFill<T>::value) {
      for (int i : range(n)) {
        ::new ((void*)(b + i)) T;
      }
    }
  }
  arr(int n, const T& init) {
    allocate(n);
    for (int i : range(n)) {
      ::new ((void*)(b + i)) T(init);
    }
  }
  arr(T* b, int n) : arr(b, b + n) {}
  arr(T* b, T* e) : b(b), n(e - b) {}
  arr(initializer_list<T> l) : arr(l.size()) {
    if (n > 0) {
      memcpy(b, l.begin(), n * sizeof(T));
    }
  }
  int size() const { return n; }
  T* begin() { return b; }
  const T* begin() const { return b; }
  T* end() { return b + n; }
  const T* end() const { return b + n; }
  arr<T> clone() const {
    arr<T> res(n);
    copy(b, b + n, res.begin());
    return res;
  }
  T& operator[](int at) { return b[at]; }
  const T& operator[](int at) const { return b[at]; }
  bool operator==(const arr& other) const {
    if (n != other.n) {
      return false;
    }
    for (int i : range(n)) {
      if (b[i] != other.b[i]) {
        return false;
      }
    }
    return true;
  }
  vector<T> view() { return vector<T>(b, b + n); }
};
void decreaseByOne() {}
template <typename T, class... Vs>
void decreaseByOne(arr<T>& array, Vs&... vs) {
  int n = array.size();
  for (int i : range(n)) {
    array[i]--;
  }
  decreaseByOne(vs...);
}
template <typename T>
class arr2d {
  T* b;
  int d1;
  int d2;
  int sz;
  void allocate(int n) {
    if (n > 0) {
      b = (T*)(::operator new(n * sizeof(T)));
    } else {
      b = nullptr;
    }
  }

 public:
  arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
    allocate(sz);
    if (NeedFill<T>::value) {
      for (int i : range(sz)) {
        ::new ((void*)(b + i)) T;
      }
    }
  }
  arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
    allocate(sz);
    for (int i : range(sz)) {
      ::new ((void*)(b + i)) T(init);
    }
  }
  arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}
  int size() const { return sz; }
  int dim1() const { return d1; }
  int dim2() const { return d2; }
  T* begin() { return b; }
  T* end() { return b + sz; }
  T& operator()(int i1, int i2) { return b[i1 * d2 + i2]; }
  const T& operator()(int i1, int i2) const { return b[i1 * d2 + i2]; }
  T& operator[](const pii& p) { return operator()(p.first, p.second); }
  const T& operator[](const pii& p) const {
    return operator()(p.first, p.second);
  }
  arr<T> operator[](int at) { return arr<T>(b + at * d2, d2); }
  vector<vector<T>> view() {
    vector<vector<T>> res(min(d1, 50));
    for (int i : range(res.size())) {
      res[i] = (*this)[i].view();
    }
    return res;
  }
};
inline bool isWhitespace(int c) { return isspace(c) || c == EOF; }
class Input {
 private:
  bool exhausted = false;
  int bufSize = 4096;
  char* buf = new char[bufSize];
  int bufRead = 0;
  int bufAt = 0;

 public:
  inline int get() {
    if (exhausted) {
      return EOF;
    }
    if (bufRead == bufAt) {
      bufRead = fread(buf, sizeof(char), bufSize, stdin);
      bufAt = 0;
    }
    if (bufRead == bufAt) {
      exhausted = true;
      return EOF;
    }
    return buf[bufAt++];
  }
  inline int peek() {
    if (exhausted) {
      return EOF;
    }
    if (bufRead == bufAt) {
      bufRead = fread(buf, sizeof(char), bufSize, stdin);
      bufAt = 0;
    }
    if (bufRead == bufAt) {
      exhausted = true;
      return EOF;
    }
    return buf[bufAt];
  }

 private:
  template <typename T>
  inline T readInteger() {
    int c = skipWhitespace();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = get();
    }
    T res = 0;
    do {
      if (!isdigit(c)) {
        return sgn * res;
      }
      res *= 10;
      res += c - '0';
      c = get();
    } while (!isWhitespace(c));
    return res * sgn;
  }
  void initArrays(int) {}
  template <typename T, class... Vs>
  void initArrays(int n, arr<T>& array, Vs&... vs) {
    array = arr<T>(n);
    initArrays(n, vs...);
  }
  template <typename T, class... Vs>
  void initArrays(int n, vector<T>&, Vs&... vs) {
    initArrays(n, vs...);
  }
  void readImpl(int) {}
  template <typename T, class... Vs>
  void readImpl(int i, arr<T>& arr, Vs&... vs) {
    arr[i] = readType<T>();
    readImpl(i, vs...);
  }
  template <typename T, class... Vs>
  void readImpl(int i, vector<T>& arr, Vs&... vs) {
    arr.push_back(readType<T>());
    readImpl(i, vs...);
  }

 public:
  inline int skipWhitespace() {
    int c;
    while (isWhitespace(c = get()) && c != EOF)
      ;
    return c;
  }
  inline int peekNext() {
    while (isWhitespace(peek()) && peek() != EOF) {
      get();
    }
    return peek();
  }
  inline int readInt() { return readInteger<int>(); }
  inline ll readLong() { return readInteger<ll>(); }
  inline unsigned readUnsigned() { return readInteger<unsigned>(); }
  string readString() {
    int c = skipWhitespace();
    if (c == EOF) {
      return "";
    }
    string res;
    do {
      res.push_back(c);
    } while (!isWhitespace(c = get()));
    return res;
  }
  arr<int> readIntArray(int size) { return readArray<int>(size); }
  arr<ll> readLongArray(int size) { return readArray<ll>(size); }
  arr<double> readDoubleArray(int size) { return readArray<double>(size); }
  arr<string> readStringArray(int size) { return readArray<string>(size); }
  arr<char> readCharArray(int size) { return readArray<char>(size); }
  template <typename T>
  T readType() {
    throw "Operation not supported";
  }
  template <typename U, typename V>
  pair<U, V> readType() {
    U first = readType<U>();
    V second = readType<V>();
    return make_pair(first, second);
  }
  template <typename T>
  arr<T> readArray(int n) {
    arr<T> res(n, T());
    for (int i : range(n)) {
      res[i] = readType<T>();
    }
    return res;
  }
  template <class... Vs>
  void readArrays(int n, Vs&... vs) {
    initArrays(n, vs...);
    for (int i : range(n)) {
      readImpl(i, vs...);
    }
  }
  template <typename U, typename V>
  arr<pair<U, V>> readArray(int n) {
    arr<pair<U, V>> res(n);
    for (int i : range(n)) {
      res[i] = readType<U, V>();
    }
    return res;
  }
  template <typename T>
  arr2d<T> readTable(int rows, int cols) {
    arr2d<T> result(rows, cols);
    for (int i : range(rows)) {
      for (int j : range(cols)) {
        result(i, j) = readType<T>();
      }
    }
    return result;
  }
  arr2d<int> readIntTable(int rows, int cols) {
    return readTable<int>(rows, cols);
  }
  arr2d<char> readCharTable(int rows, int cols) {
    return readTable<char>(rows, cols);
  }
  string readLine() {
    int c = get();
    if (c == EOF) {
      return "";
    }
    string res;
    do {
      res.push_back(c);
      c = get();
    } while (c != '\n' && c != '\r' && c != EOF);
    return res;
  }
  inline double readDouble() {
    int c = skipWhitespace();
    int sgn = 1;
    if (c == '-') {
      sgn = -1;
      c = get();
    }
    double res = 0;
    do {
      if (tolower(c) == 'e') {
        return sgn * res * dPower(double(10), readInt());
      }
      if (!isdigit(c)) {
        return sgn * res;
      }
      res *= 10;
      res += c - '0';
      c = get();
    } while (!isWhitespace(c) && c != '.');
    if (c == '.') {
      double add = 0;
      int length = 0;
      c = get();
      do {
        if (tolower(c) == 'e') {
          return sgn * (res + add * dPower(double(10), -length)) *
                 dPower(double(10), readInt());
        }
        if (!isdigit(c)) {
          res += add * dPower(10, -length);
          return res * sgn;
        }
        add *= 10;
        add += c - '0';
        length++;
        c = get();
      } while (!isWhitespace(c));
      res += add * dPower(double(10), -length);
    }
    return res * sgn;
  }
  inline char readChar() {
    int c = skipWhitespace();
    if (c == EOF) {
      return 0;
    }
    return c;
  }
  inline bool isExhausted() { return exhausted; }
  inline void setBufSize(int newBufSize) {
    if (newBufSize > bufSize) {
      char* newBuf = new char[newBufSize];
      memcpy(newBuf, buf, bufSize);
      buf = newBuf;
    }
    bufSize = newBufSize;
  }
};
template <>
inline double Input::readType() {
  return readDouble();
}
template <>
inline int Input::readType() {
  return readInt();
}
template <>
inline ll Input::readType() {
  return readLong();
}
template <>
inline unsigned Input::readType() {
  return readUnsigned();
}
template <>
inline char Input::readType() {
  return readChar();
}
template <>
inline string Input::readType() {
  return readString();
}
Input in;
class Output {
 private:
  ostream* out;
  template <typename T>
  inline void printSingle(const T& value) {
    *out << value;
  }
  template <typename T>
  void printSingle(const vector<T>& array) {
    size_t n = array.size();
    for (int i : range(n)) {
      *out << array[i];
      if (i + 1 != n) {
        *out << ' ';
      }
    }
  }
  template <typename T>
  void printSingle(const arr<T>& array) {
    int n = array.size();
    for (int i : range(n)) {
      *out << array[i];
      if (i + 1 != n) {
        *out << ' ';
      }
    }
  }
  template <typename T>
  void printSingle(const arr2d<T>& array) {
    size_t n = array.dim1();
    size_t m = array.dim2();
    for (int i : range(n)) {
      for (int j : range(m)) {
        *out << array(i, j);
        if (j + 1 != m) {
          *out << ' ';
        }
      }
      if (i + 1 != n) {
        *out << '\n';
      }
    }
  }
  template <typename T, typename U>
  inline void printSingle(const pair<T, U>& value) {
    *out << value.first << ' ' << value.second;
  }

 public:
  bool autoflush;
  Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
    setPrecision(20);
  }
  void setOut(ostream& nOut) {
    out = &nOut;
    setPrecision(20);
  }
  inline void print() {}
  template <typename T, typename... Targs>
  inline void print(const T& first, const Targs... args) {
    printSingle(first);
    if (sizeof...(args) != 0) {
      *out << ' ';
      print(args...);
    }
    if (autoflush) {
      flush();
    }
  }
  template <typename... Targs>
  inline void printLine(const Targs... args) {
    print(args...);
    *out << '\n';
    if (autoflush) {
      flush();
    }
  }
  inline void flush() { out->flush(); }
  inline void setPrecision(int digs) { *out << fixed << setprecision(digs); }
};
Output out(cout, false);
Output err(cerr, true);
inline bool isSubset(unsigned set, unsigned subSet) {
  return (set & subSet) == subSet;
}
inline int bitCount(unsigned x) { return __builtin_popcount(x); }
inline int bitCount(ull x) { return __builtin_popcountll(x); }
inline int bitCount(uli x) {
  return __builtin_popcountll(x) + __builtin_popcountll(x >> 64);
}
inline int highestOneBit(unsigned x) {
  return 1 << (31 - __builtin_clz(x | 1));
}
inline int binaryDigits(unsigned x) { return 32 - __builtin_clz(x | 1); }
inline ull setBit(ull mask, int bit) {
  mask |= ull(1) << bit;
  return mask;
}
inline unsigned setBit(unsigned mask, int bit) {
  mask |= unsigned(1) << bit;
  return mask;
}
inline uli setBit(uli mask, int bit) {
  mask |= uli(1) << bit;
  return mask;
}
inline ull unsetBit(ull mask, int bit) {
  mask &= ~(ull(1) << bit);
  return mask;
}
inline unsigned unsetBit(unsigned mask, int bit) {
  mask &= ~(unsigned(1) << bit);
  return mask;
}
inline uli unsetBit(uli mask, int bit) {
  mask &= ~(uli(1) << bit);
  return mask;
}
inline bool isSet(ull mask, int bit) { return mask >> bit & 1; }
inline bool isSet(unsigned mask, int bit) { return mask >> bit & 1; }
inline bool isSet(uli mask, int bit) { return mask >> bit & 1; }
inline unsigned allBits(int n) { return (1u << n) - 1; }
inline ull allBitsLL(int n) { return (1ull << n) - 1; }
const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
const int MODF = 998244353;
int mod = MOD7;
ll gcd(ll a, ll b, ll& x, ll& y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  int d = gcd(b % a, a, y, x);
  x -= (b / a) * y;
  return d;
}
class modint {
 public:
  int n;
  modint() : n(0) {}
  modint(ll n, bool special = false) {
    if (special) {
      this->n = -1;
      return;
    }
    if (n >= 0 && n < mod) {
      this->n = n;
      return;
    }
    n %= mod;
    if (n < 0) {
      n += mod;
    }
    this->n = n;
  }
  modint& operator+=(const modint& other) {
    n += other.n;
    if (n >= mod) {
      n -= mod;
    }
    return *this;
  }
  modint& operator-=(const modint& other) {
    n -= other.n;
    if (n < 0) {
      n += mod;
    }
    return *this;
  }
  modint& operator*=(const modint& other) {
    n = ll(n) * other.n % mod;
    return *this;
  }
  modint& operator/=(const modint& other) { return *this *= other.inverse(); }
  modint operator-() {
    if (n == 0) {
      return 0;
    }
    return modint(mod - n);
  }
  modint inverse() const {
    ll x, y;
    ll g = gcd(ll(n), ll(mod), x, y);
    return x;
  }
  int log(modint alpha);
};
modint nullModint(-1, true);
modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
ostream& operator<<(ostream& out, const modint& val) { return out << val.n; }
bool operator==(const modint& a, const modint& b) { return a.n == b.n; }
bool operator!=(const modint& a, const modint& b) { return a.n != b.n; }
namespace std {
template <>
struct hash<modint> {
  size_t operator()(const modint& n) const { return n.n; }
};
}  // namespace std
int modint::log(modint alpha) {
  unordered_map<modint, int> base;
  int exp = 0;
  modint pow = 1;
  modint inv = *this;
  modint alInv = alpha.inverse();
  while (exp * exp < mod) {
    if (inv == 1) {
      return exp;
    }
    base[inv] = exp++;
    pow *= alpha;
    inv *= alInv;
  }
  modint step = pow;
  for (int i = 1;; i++) {
    if (base.count(pow)) {
      return exp * i + base[pow];
    }
    pow *= step;
  }
}
template <typename T>
T gcd(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b != 0) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <typename T>
T power(const T& a, ll b) {
  if (b == 0) {
    return 1;
  }
  if ((b & 1) == 0) {
    T res = power(a, b >> 1);
    return res * res;
  } else {
    return power(a, b - 1) * a;
  }
}
template <typename T>
arr<T> factorials(int length) {
  arr<T> result(length);
  if (length > 0) {
    result[0] = 1;
  }
  for (int i = 1; i < length; i++) {
    result[i] = result[i - 1] * i;
  }
  return result;
}
template <typename T>
T factorial(int n) {
  T result = 1;
  for (int i = 2; i <= n; i++) {
    result *= i;
  }
  return result;
}
template <typename T>
arr<T> powers(T base, int length) {
  arr<T> result(length);
  if (length > 0) {
    result[0] = 1;
  }
  for (int i = 1; i < length; i++) {
    result[i] = result[i - 1] * base;
  }
  return result;
}
class ReverseNumberIterator : public NumberIterator {
 public:
  ReverseNumberIterator(int v) : NumberIterator(v) {}
  ReverseNumberIterator& operator++() {
    --v;
    return *this;
  }
};
class RevRange : pii {
 public:
  RevRange(int begin, int end) : pii(begin - 1, min(begin, end) - 1) {}
  RevRange(int n) : pii(n - 1, min(n, 0) - 1) {}
  ReverseNumberIterator begin() { return first; }
  ReverseNumberIterator end() { return second; }
};
class IBitovayaMagiya {
 public:
  void solve() {
    int n = in.readInt();
    int k = in.readInt();
    int c = in.readInt();
    auto a = in.readArray<unsigned>(n);
    unsigned base = 0;
    arr<vi> where(c + 1);
    for (unsigned i : a) {
      for (int j : range(c + 1)) {
        if ((i & allBits(j)) >= k) {
          where[j].push_back(i & allBits(j));
          base ^= i;
          break;
        }
      }
    }
    mod = MODF;
    arr2d<modint> cc(k + 1, k + 1, 0);
    for (int i : range(k + 1)) {
      cc(i, 0) = 1;
      for (int j : range(1, i + 1)) {
        cc(i, j) = cc(i - 1, j - 1) + cc(i - 1, j);
      }
    }
    arr2d<modint> answer(k + 1, 1 << c, 0);
    answer(0, 0) = 1;
    for (int i : range(c + 1)) {
      err.printLine("i =", i);
      sort((where[i]).begin(), (where[i]).end());
      for (unsigned j : where[i]) {
        if (j >= (1 << i) || j < k) {
          while (true)
            ;
        }
        for (int l : RevRange(k)) {
          for (int o : range(1 << i)) {
            if (answer(l, o) == 0) {
              continue;
            }
            for (int m : range(1, k + 1 - l)) {
              modint cf = cc(l + m, l);
              answer(l + m, o ^ (j - m) ^ j) += answer(l, o) * cf;
            }
          }
        }
      }
    }
    arr<modint> res(1 << c);
    modint cf = power(modint(n), k).inverse();
    for (int i : range(1 << c)) {
      res[i ^ base] = answer(k, i) * cf;
    }
    out.printLine(res);
  }
};
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  IBitovayaMagiya solver;
  solver.solve();
  fflush(stdout);
  return 0;
}