Problem: A group of n merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the n mugs must be the same.

Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has a1 milliliters of the drink, the second one has a2 milliliters and so on. The bottle has b milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.

Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously: 

  * there were b milliliters poured in total. That is, the bottle need to be emptied; 
  * after the process is over, the volumes of the drink in the mugs should be equal. 

Input

The first line contains a pair of integers n, b (2 ≤ n ≤ 100, 1 ≤ b ≤ 100), where n is the total number of friends in the group and b is the current volume of drink in the bottle. The second line contains a sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 100), where ai is the current volume of drink in the i-th mug.

Output

Print a single number "-1" (without the quotes), if there is no solution. Otherwise, print n float numbers c1, c2, ..., cn, where ci is the volume of the drink to add in the i-th mug. Print the numbers with no less than 6 digits after the decimal point, print each ci on a single line. Polycarpus proved that if a solution exists then it is unique.

Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma.

Examples

Input

5 50
1 2 3 4 5


Output

12.000000
11.000000
10.000000
9.000000
8.000000


Input

2 2
1 100


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
const double pi = acos(-1.0);
const double eps = 1e-11;
const int p = 1000000007;
int countbit(int n) { return n == 0 ? 0 : countbit(n / 2) + n % 2; }
int lowbit(int n) { return (n ^ (n - 1)) & n; }
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
long long toInt64(string s) {
  istringstream sin(s);
  long long t;
  sin >> t;
  return t;
}
template <typename T>
T sqr(T n) {
  return n * n;
}
template <typename T>
void out(T& v) {
  for (int i = 0; i < v.size(); i++) cout << v[i] << ' ';
  cout << endl;
}
int main() {
  double start = static_cast<double>(clock());
  int n, b;
  cin >> n >> b;
  vector<double> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  double all = accumulate(a.begin(), a.end(), double(b));
  double perPerson = all / n;
  bool ok = true;
  for (int i = 0; i < n; i++)
    if (a[i] - perPerson > eps) {
      cout << -1 << endl;
      ok = false;
      break;
    }
  if (ok)
    for (int i = 0; i < n; i++) {
      cout.setf(ios::fixed, ios::floatfield);
      cout.precision(8);
      cout << perPerson - a[i] << endl;
    }
  return 0;
}