Problem: Eugeny has n cards, each of them has exactly one integer written on it. Eugeny wants to exchange some cards with Nikolay so that the number of even integers on his cards would equal the number of odd integers, and that all these numbers would be distinct. 

Nikolay has m cards, distinct numbers from 1 to m are written on them, one per card. It means that Nikolay has exactly one card with number 1, exactly one card with number 2 and so on. 

A single exchange is a process in which Eugeny gives one card to Nikolay and takes another one from those Nikolay has. Your task is to find the minimum number of card exchanges and determine which cards Eugeny should exchange.

Input

The first line contains two integers n and m (2 ≤ n ≤ 2·105, 1 ≤ m ≤ 109) — the number of cards Eugeny has and the number of cards Nikolay has. It is guaranteed that n is even.

The second line contains a sequence of n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the numbers on Eugeny's cards.

Output

If there is no answer, print -1.

Otherwise, in the first line print the minimum number of exchanges. In the second line print n integers — Eugeny's cards after all the exchanges with Nikolay. The order of cards should coincide with the card's order in the input data. If the i-th card wasn't exchanged then the i-th number should coincide with the number from the input data. Otherwise, it is considered that this card was exchanged, and the i-th number should be equal to the number on the card it was exchanged to.

If there are multiple answers, it is allowed to print any of them.

Examples

Input

6 2
5 6 7 9 4 5


Output

1
5 6 7 9 4 2 


Input

8 6
7 7 7 7 8 8 8 8


Output

6
7 2 4 6 8 1 3 5 


Input

4 1
4 2 1 10


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline namespace Infinity {
inline namespace Constant {
constexpr const int eof = EOF;
constexpr const int maxint = INT_MAX;
constexpr const long long maxll = LLONG_MAX;
constexpr const double eps = DBL_EPSILON;
}  // namespace Constant
inline namespace TypeDefine {
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
template <typename T = int>
using Pair = pair<T, T>;
template <typename T = int>
using PairList = vector<Pair<T>>;
template <typename T = vector<int>>
using Iter = typename T::iterator;
}  // namespace TypeDefine
inline namespace IO {
const char LF = '\n';
const char SP = ' ';
int dbl_prec = 10;
int ldbl_prec = 18;
inline void write(const int n) { printf("%d", n); }
inline void write(const unsigned n) { printf("%u", n); }
inline void write(const int64_t n) { printf("%" PRId64, n); }
inline void write(const uint64_t n) { printf("%" PRIu64, n); }
inline void write(const double a) { printf("%.*f", dbl_prec, a); }
inline void write(const long double a) { printf("%.*Lf", ldbl_prec, a); }
inline void write(const char c) { printf("%c", c); }
inline void write(const char s[]) { printf("%s", s); }
inline void write(const string &s) { printf("%s", s.data()); }
template <typename T>
inline void writeSP(const T a) {
  write(a);
  write(SP);
}
template <typename T, typename U>
inline void write(const pair<T, U> &p) {
  writeSP(p.first);
  write(p.second);
}
template <class T>
inline void write(const T a) {
  for (auto i = a.begin(); i != a.end(); i++) {
    if (i != a.begin()) write(SP);
    write(*i);
  }
}
template <typename T>
inline void write(initializer_list<T> list) {
  for (auto i = list.begin(); i != list.end(); i++) {
    if (i != list.begin()) write(SP);
    write(*i);
  }
}
template <typename T>
inline void writer(T begin, T end) {
  for (write(*begin++); begin != end; ++begin) write(SP), write(*begin);
}
inline void writeln() { write(LF); }
inline void writeSP() { write(SP); }
template <typename T>
inline void writeln(const T &a) {
  write(a);
  write(LF);
}
template <typename T>
inline void writeln(initializer_list<T> list) {
  for (auto i = list.begin(); i != list.end(); i++) {
    if (i != list.begin()) write(SP);
    write(*i);
  }
  write(LF);
}
template <class T>
inline void writelns(const T &a) {
  for (auto n : a) writeln(n);
}
template <typename T, typename... types>
inline void write(const T &a, const types &...args) {
  write(a);
  write(args...);
}
template <typename... types>
inline void writeln(const types &...args) {
  write(args...);
  write(LF);
}
template <typename... types>
inline void writeSP(const types &...args) {
  write(args...);
  write(SP);
}
inline void writelnYN(bool b) { writeln(b ? "YES" : "NO"); }
inline void writelnyn(bool b) { writeln(b ? "Yes" : "No"); }
string caseN(int n, bool sharp = true, bool space = true) {
  return string("Case ") + (sharp ? "#" : "") + to_string(n) + ":" +
         (space ? " " : "");
}
inline int read(int &n) { return scanf("%d", &n); }
inline int read(int64_t &n) { return scanf("%" SCNd64, &n); }
inline char getcc() {
  char c;
  do c = getchar();
  while (isspace(c));
  return c;
}
inline int getint() {
  int n;
  read(n);
  return n;
}
inline int64_t getll() {
  int64_t n;
  read(n);
  return n;
}
inline double getdbl() {
  double n;
  scanf("%lf", &n);
  return n;
}
inline pair<int, int> getpair() {
  pair<int, int> p;
  scanf("%d%d", &p.first, &p.second);
  return p;
}
inline vector<int> getints(int n) {
  vector<int> v(n);
  for (int &i : v) i = getint();
  return v;
}
inline vector<pair<int, int>> getpairs(int n) {
  vector<pair<int, int>> v(n);
  for (pair<int, int> &p : v) {
    p = getpair();
  }
  return v;
}
inline void read(string &str, unsigned size) {
  char s[++size];
  scanf("%s", s);
  str.assign(s);
}
inline string getstr(unsigned size = 0x100000) {
  string s;
  read(s, size);
  return s;
}
inline string getln(unsigned size = 0x100000) {
  char s[++size];
  scanf("%[^\n]", s);
  getchar();
  return s;
}
}  // namespace IO
inline namespace BattleLab {
class Range {
  class RangeIterator {
   public:
    RangeIterator(int current = 0, int step = 1)
        : current(current), step(step) {}
    bool operator!=(const RangeIterator &iterator) const {
      return current < iterator.current;
    }
    int operator*() const { return current; }
    RangeIterator operator++() { return {current += step, step}; }

   protected:
    int current, step;
  };

 public:
  Range(int to, int from = 0, int step = 1) : from(from), to(to), step(step) {}
  RangeIterator begin() const { return {from, step}; }
  RangeIterator end() const { return {to, step}; }

 protected:
  int from, to, step;
};
Range range(int to) { return {to}; }
Range range(int from, int to) { return {to, from}; }
Range range(int from, int to, int step) { return {to, from, step}; }
}  // namespace BattleLab
inline namespace Miscelleneous {
inline constexpr int ctoi(const char c) { return c - '0'; }
inline constexpr char itoc(const int n) { return n + '0'; }
inline int dtoi(const double d) { return round(d); }
template <typename T>
inline constexpr bool in(T x, T l, T r) {
  return l <= x && x <= r;
}
template <typename T>
inline constexpr T tristate(int val, T nag, T zero, T pos) {
  return val > 0 ? pos : val < 0 ? nag : zero;
}
template <class T>
inline int size(const T &a) {
  return a.size();
}
template <class T>
inline void sort(T &a) {
  sort(a.begin(), a.end());
}
template <class T1, class T2>
inline void sort(T1 &a, T2 comp) {
  sort(a.begin(), a.end(), comp);
}
template <class T1, typename T2>
inline int lbound(const T1 &a, const T2 k) {
  return lower_bound(a.begin(), a.end(), k) - a.begin();
}
template <class T1, typename T2>
inline int ubound(const T1 &a, const T2 k) {
  return upper_bound(a.begin(), a.end(), k) - a.begin();
}
template <class T1, class T2>
inline int count(T1 &a, T2 k) {
  return ubound(a, k) - lbound(a, k);
}
template <typename T>
inline void clear(T &a) {
  memset(a, 0, sizeof a);
}
template <typename T>
T gcd(T a, T b) {
  while (b) {
    T t = a % b;
    a = b;
    b = t;
  }
  return a;
}
template <typename T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
long long qpow(long long a, long long b, long long c) {
  return b ? qpow(a * a % c, b >> 1, c) * (b & 1 ? a : 1) % c : 1;
}
template <typename T>
T exGcd(T a, T b, T &x, T &y) {
  T d = a;
  if (b) {
    d = exGcd(b, a % b, y, x);
    y -= a / b * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
template <typename T>
inline constexpr T mps(T l, T r, T k) {
  return ((r - (r % k + k) % k) - (l + (k - l % k) % k)) / k + 1;
}
template <typename T>
inline constexpr T sgn(T a) {
  return a ? a > 0 ? 1 : -1 : 0;
}
template <typename T>
inline constexpr T sq(T a) {
  return a * a;
}
template <typename T>
inline constexpr bool odd(T a) {
  return bool(a % 2);
}
template <typename T>
inline constexpr bool even(T a) {
  return !bool(a % 2);
}
template <typename T1, typename T2>
inline constexpr T1 smod(T1 x, T2 m) {
  return x > m ? x - m : x + m < m ? x + m : x;
}
vector<int> repetend(vector<int> a) {
  vector<int> p(a.size(), -1);
  for (unsigned i = 0; i < a.size(); i++)
    if (p[i] == -1) {
      int c = 1;
      for (unsigned j = a[i]; j != i; j = a[j]) ++c;
      p[i] = c;
      for (unsigned j = a[i]; j != i; j = a[j]) p[j] = c;
    }
  return p;
}
template <typename T>
inline constexpr T lmiddle(T first, T last) {
  return first + (last - first) / 2;
}
template <typename T>
inline constexpr T rmiddle(T first, T last) {
  return last - (last - first) / 2;
}
template <typename T, typename F>
T dichotomy(T l, T r, F check, T prec = 1) {
  while (r - l > prec) {
    T m = lmiddle(l, r);
    (check(m) ? l : r) = m;
  }
  return l;
}
template <typename T, typename F>
T dichotomy2(T l, T r, F check, T prec = 1) {
  while (r - l > prec) {
    T m = rmiddle(l, r);
    (check(m) ? r : l) = m;
  }
  return r;
}
bool contains(const string &s, const string &t) {
  return s.find(t) != string::npos;
}
template <typename T>
bool contains(const T &s, typename T::value_type t) {
  for (typename T::value_type c : s)
    if (c == t) return true;
  return false;
}
template <typename T>
bool contains(const initializer_list<T> s, T t) {
  return find(s.begin(), s.end(), t) != s.end();
}
}  // namespace Miscelleneous
}  // namespace Infinity
struct Node {
  int val;
  int id;
  Node(int val = 0, int id = 0) : val(val), id(id) {}
};
int main() {
  int n = getint(), m = getint();
  vector<Node> a;
  for (int i : range(n)) {
    a.emplace_back(getint(), i);
  }
  sort(a, [](const Node &n1, const Node &n2) { return n1.val < n2.val; });
  int co = count_if(a.begin(), a.end(),
                    [](const Node &n) { return odd(n.val); }),
      ce = count_if(a.begin(), a.end(),
                    [](const Node &n) { return even(n.val); });
  set<int> occ;
  for (int i : range(n)) {
    occ.insert(a[i].val);
  }
  int no = 1, ne = 2, cc = 0;
  vector<int> ep;
  for (int i : range(n)) {
    if (i != n - 1 && a[i].val == a[i + 1].val) {
      ep.push_back(i);
      if (odd(a[i].val)) {
        --co;
      } else {
        --ce;
      }
    }
  }
  auto nextOdd = [&]() {
    while (occ.count(no)) {
      no += 2;
      if (no > m) {
        throw -1;
      }
    }
    occ.insert(no);
    ++co;
    ++cc;
    return no;
  };
  auto nextEven = [&]() {
    while (occ.count(ne)) {
      ne += 2;
      if (ne > m) {
        throw -1;
      }
    }
    occ.insert(ne);
    ++ce;
    ++cc;
    return ne;
  };
  try {
    for (int p : ep) {
      if (co <= ce) {
        a[p].val = nextOdd();
      } else {
        a[p].val = nextEven();
      }
    }
    if (co != ce) {
      for (int i : range(n)) {
        if (co < ce && even(a[i].val)) {
          --ce;
          a[i].val = nextOdd();
        }
        if (ce < co && odd(a[i].val)) {
          --co;
          a[i].val = nextEven();
        }
      }
    }
    sort(a, [](const Node &n1, const Node &n2) { return n1.id < n2.id; });
    writeln(cc);
    for (int i : range(n)) {
      writeSP(a[i].val);
    }
  } catch (int e) {
    writeln(e);
  }
  return 0;
}