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;
struct edge {
  long long to, cost;
  edge() {}
  edge(long long a, long long b) { to = a, cost = b; }
};
const long long dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
const long long mod = 1000000007;
struct mint {
  long long x = 0;
  mint(long long y = 0) {
    x = y;
    if (x < 0 || x >= mod) x = (x % mod + mod) % mod;
  }
  mint(const mint& ope) { x = ope.x; }
  mint operator-() { return mint(-x); }
  mint operator+(const mint& ope) { return mint(x) += ope; }
  mint operator-(const mint& ope) { return mint(x) -= ope; }
  mint operator*(const mint& ope) { return mint(x) *= ope; }
  mint operator/(const mint& ope) { return mint(x) /= ope; }
  mint& operator+=(const mint& ope) {
    x += ope.x;
    if (x >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint& ope) {
    x += mod - ope.x;
    if (x >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint& ope) {
    x *= ope.x, x %= mod;
    return *this;
  }
  mint& operator/=(const mint& ope) {
    long long n = mod - 2;
    mint mul = ope;
    while (n) {
      if (n & 1) *this *= mul;
      mul *= mul;
      n >>= 1;
    }
    return *this;
  }
  mint inverse() { return mint(1) / *this; }
  bool operator==(const mint& ope) { return x == ope.x; }
  bool operator!=(const mint& ope) { return x != ope.x; }
};
mint modpow(mint a, long long n) {
  if (n == 0) return mint(1);
  if (n % 2)
    return a * modpow(a, n - 1);
  else
    return modpow(a * a, n / 2);
}
istream& operator>>(istream& is, mint& ope) {
  long long t;
  is >> t, ope.x = t;
  return is;
}
ostream& operator<<(ostream& os, mint& ope) { return os << ope.x; }
ostream& operator<<(ostream& os, const mint& ope) { return os << ope.x; }
bool exceed(long long x, long long y, long long m) { return x >= m / y + 1; }
void mark() { cout << "*" << endl; }
void yes() { cout << "YES" << endl; }
void no() { cout << "NO" << endl; }
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long digitnum(long long x, long long b = 10) {
  long long ret = 0;
  for (; x; x /= b) ret++;
  return ret;
}
long long digitsum(long long x, long long b = 10) {
  long long ret = 0;
  for (; x; x /= b) ret += x % b;
  return ret;
}
string tostr(long long x) {
  string ret;
  for (; x; x /= 10) ret += x % 10 + '0';
  reverse(ret.begin(), ret.end());
  return ret;
}
long long toint(string& s) {
  long long ret = 0;
  for (auto c : s) ret *= 10, ret += c - '0';
  return ret;
}
template <typename T>
void uniq(T& vec) {
  sort(vec.begin(), vec.end());
  vec.erase(unique(vec.begin(), vec.end()), vec.end());
}
template <typename T>
ostream& operator<<(ostream& os, vector<T>& vec) {
  for (int i = 0; i < vec.size(); i++)
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, deque<T>& deq) {
  for (int i = 0; i < deq.size(); i++)
    os << deq[i] << (i + 1 == deq.size() ? "" : " ");
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, pair<T, U>& pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& pair_var) {
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, map<T, U>& map_var) {
  for (typename map<T, U>::iterator itr = map_var.begin(); itr != map_var.end();
       itr++) {
    os << "(" << itr->first << ", " << itr->second << ")";
    itr++;
    if (itr != map_var.end()) os << ",";
    itr--;
  }
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, set<T>& set_var) {
  for (typename set<T>::iterator itr = set_var.begin(); itr != set_var.end();
       itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, multiset<T>& set_var) {
  for (typename multiset<T>::iterator itr = set_var.begin();
       itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}
template <typename T>
void outa(T a[], long long s, long long t) {
  for (long long i = s; i <= t; i++) {
    cout << a[i];
    if (i < t) cout << " ";
  }
  cout << endl;
}
void dump_func() { cout << endl; }
template <class Head, class... Tail>
void dump_func(Head&& head, Tail&&... tail) {
  cout << head;
  if (sizeof...(Tail) > 0) cout << " ";
  dump_func(std::move(tail)...);
}
long long n, m;
long long a[200005];
set<long long> S;
int main(void) {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m;
  for (long long(i) = (1); (i) <= (n); (i)++) cin >> a[i];
  for (long long(i) = (1); (i) <= (n); (i)++) {
    if (S.count(a[i]))
      a[i] = 0;
    else
      S.insert(a[i]);
  }
  long long odd = 0, even = 0;
  for (long long(i) = (1); (i) <= (n); (i)++) {
    if (a[i] == 0) continue;
    if (a[i] % 2) {
      if (odd >= n / 2)
        a[i] = 0;
      else
        odd++;
    } else {
      if (even >= n / 2)
        a[i] = 0;
      else
        even++;
    }
  }
  long long ans = 0;
  for (long long(i) = (1); (i) <= (n); (i)++)
    if (a[i] == 0) ans++;
  long long nodd = 1, neven = 2;
  for (long long(i) = (1); (i) <= (n); (i)++) {
    if (a[i]) continue;
    if (odd < n / 2) {
      while (nodd <= m && S.count(nodd)) nodd += 2;
      if (nodd > m) {
        dump_func(-1);
        return 0;
      }
      a[i] = nodd;
      nodd += 2;
      odd++;
    } else {
      while (neven <= m && S.count(neven)) neven += 2;
      if (neven > m) {
        dump_func(-1);
        return 0;
      }
      a[i] = neven;
      neven += 2;
      even++;
    }
  }
  dump_func(ans);
  outa(a, 1, n);
  return 0;
}