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>
using namespace std;
const long long int maxN = 1E2 + 10;
const long long int mod = 1E9 + 7;
pair<long double, long double> p[maxN];
int32_t main() {
  long double n, b;
  cin >> n >> b;
  for (long long int i = 0; i < n; ++i) cin >> p[i].first;
  for (long long int i = 0; i < n; ++i) p[i].second = b / n;
  long double sum = 0;
  for (long long int i = 0; i < n; ++i) sum += p[i].first;
  sum /= n;
  for (long long int i = 0; i < n; ++i) {
    if (p[i].first > sum)
      p[i].second -= (p[i].first - sum);
    else
      p[i].second += (sum - p[i].first);
  }
  for (long long int i = 0; i < n; ++i) {
    if (p[i].second < -(long double)0.00000001) {
      cout << -1 << "\n";
      return 0;
    } else if (p[i].second < 0)
      p[i].second = 0;
  }
  for (long long int i = 0; i < n; ++i)
    cout << fixed << setprecision(8) << p[i].second << "\n";
  return 0;
}