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 double pi = 3.141592653589793;
const int INF = 2000000000;
const int mod = 1000000007;
const int N = 100000000;
const int base = 10;
vector<int> read(string s) {
  vector<int> a;
  for (int i = (int)s.length(); i > 0; i -= 1)
    if (i < 1)
      a.push_back(atoi(s.substr(0, i).c_str()));
    else
      a.push_back(atoi(s.substr(i - 1, 1).c_str()));
  return a;
}
vector<int> add(vector<int> a, vector<int> b) {
  int carry = 0;
  for (size_t i = 0; i < max(a.size(), b.size()) || carry; ++i) {
    if (i == a.size()) a.push_back(0);
    a[i] += carry + (i < b.size() ? b[i] : 0);
    carry = a[i] >= base;
    if (carry) a[i] -= base;
  }
  return a;
}
vector<int> mul(vector<int> a, int b) {
  int carry = 0;
  for (size_t i = 0; i < a.size() || carry; ++i) {
    if (i == a.size()) a.push_back(0);
    long long cur = carry + a[i] * 1ll * b;
    a[i] = int(cur % base);
    carry = int(cur / base);
  }
  while (a.size() > 1 && a.back() == 0) a.pop_back();
  return a;
}
int main() {
  long n, k;
  int c;
  vector<int> a;
  double max;
  max = 0;
  cin >> n >> k;
  for (int(i) = (0); (i) < (n); (i)++) {
    cin >> c;
    a.push_back(c);
    if (c > max) {
      max = c;
    }
  }
  long res = 0;
  for (int(i) = (0); (i) < (n); (i)++) {
    res += max - a[i];
  }
  if (res <= k) {
    max += double(k - res) / n;
    for (int(i) = (0); (i) < (n); (i)++) {
      printf("%.8f\n", max - a[i]);
    }
  } else {
    cout << -1;
    return 0;
  }
  return 0;
}