Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1, a2, ..., an. His teapot stores w milliliters of tea (w ≤ a1 + a2 + ... + an). Polycarp wants to pour tea in cups in such a way that:

  * Every cup will contain tea for at least half of its volume 
  * Every cup will contain integer number of milliliters of tea 
  * All the tea from the teapot will be poured into cups 
  * All friends will be satisfied. 



Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai > aj.

For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.

Input

The first line contains two integer numbers n and w (1 ≤ n ≤ 100, <image>).

The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 100).

Output

Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them.

If it's impossible to pour all the tea and satisfy all conditions then output -1.

Examples

Input

2 10
8 7


Output

6 4 


Input

4 4
1 1 1 1


Output

1 1 1 1 


Input

3 10
9 8 10


Output

-1

Note

In the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available.
#include <bits/stdc++.h>
using namespace std;
long long int Mmax(long long int a, long long int b) {
  if (a > b) return a;
  return b;
}
long long int Mmin(long long int a, long long int b) {
  if (a < b) return a;
  return b;
}
long long int nod(long long int a, long long int b) {
  while (a && b) {
    if (a > b)
      a %= b;
    else
      b %= a;
  }
  return Mmax(a, b);
}
long long int nok(long long int a, long long int b) {
  return a * b / nod(a, b);
}
bool IsPrime(long long int x) {
  if (x < 2) return false;
  long long int X = sqrt(x), i;
  for (i = 2; i <= X; i++)
    if (x % i == 0) return false;
  return true;
}
void hanoi(int n, int A, int C, int B) {
  if (n == 1) {
    cout << n << " " << A << " " << C << endl;
  } else {
    hanoi(n - 1, A, B, C);
    cout << n << " " << A << " " << C << endl;
    hanoi(n - 1, B, C, A);
  }
}
string pr2(string a, int d) {
  if (d == 0) return "0";
  string b;
  long long int sz = a.size(), i, prenos = 0;
  for (i = 0; i < sz; i++) {
    b[i] = a[i];
  }
  for (i = sz - 1; i > -1; i--) {
    a[i] = ((b[i] - '0') * d + prenos) % 10 + '0';
    prenos = ((b[i] - '0') * d + prenos) / 10;
  }
  if (prenos) a = char(prenos + '0') + a;
  return a;
}
string sum(string a, string b) {
  bool carry = false;
  long long int i, sz1, sz2, maxsz, minsz;
  string c, d;
  sz1 = a.size();
  sz2 = b.size();
  maxsz = max(sz1, sz2);
  minsz = min(sz1, sz2);
  while (sz1 < maxsz) {
    sz1++;
    a = '0' + a;
  }
  while (sz2 < maxsz) {
    sz2++;
    b = '0' + b;
  }
  for (i = maxsz - 1; i > -1; i--) {
    d = char((a[i] + b[i] - 96 + carry) % 10 + 48) + d;
    if (a[i] + b[i] - 96 + carry > 9)
      carry = true;
    else
      carry = false;
  }
  if (carry == true) d = char('1') + d;
  return d;
}
string pr(string a, string b) {
  string res = "0", p, p2;
  int sz = a.size(), x = 0;
  for (sz = a.size(); sz > 0; sz--, x++) {
    int d = a[sz - 1] - '0';
    a = a.erase(sz - 1, 1);
    p2 = pr2(b, d);
    p2 += p;
    res = sum(res, p2);
    p += "0";
  }
  return res;
}
bool vesokosna(long long int x) {
  return (x % 4 == 0 && x % 100 || x % 400 == 0);
}
long long int reverse(long long int x) {
  long long int mirror = 0;
  while (x) {
    mirror = mirror * 10 + x % 10;
    x /= 10;
  }
  return mirror;
}
long long int ost(string x, long long int k) {
  long long int num = 0, i, sz = x.size();
  for (i = 0; i < sz; i++) {
    num = num * 10;
    num += x[i] - '0';
    num %= k;
  }
  return num;
}
int n, w;
struct help {
  int a, I;
};
help h[128];
bool cmp(help a, help b) {
  if (a.a < b.a) return true;
  if (a.a > b.a) return false;
  if (a.I < b.I) return true;
  if (a.I > b.I) return false;
  return true;
}
int maxsum, minsum;
int answer[128];
int main() {
  cin >> n >> w;
  int i;
  for (i = 0; i < n; i++) {
    cin >> h[i].a;
    maxsum += h[i].a;
    minsum += (h[i].a + 1) / 2;
    h[i].I = i;
  }
  if (w < minsum) {
    cout << -1 << endl;
    return 0;
  }
  if (w > maxsum) {
    cout << -1 << endl;
    return 0;
  }
  w -= minsum;
  sort(h, h + n, cmp);
  for (i = 0; i < n; i++) {
    answer[h[i].I] = (h[i].a + 1) / 2;
  }
  for (i = n - 1; i >= 0; i--) {
    if (h[i].a - answer[h[i].I] < w)
      w -= h[i].a - answer[h[i].I], answer[h[i].I] = h[i].a;
    else {
      answer[h[i].I] += w, w = 0;
      break;
    }
  }
  for (i = 0; i < n; i++) cout << answer[i] << " ";
  cout << endl;
  return 0;
}
