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 INF = 1600000000000000000LL;
const int MOD = 1000000007;
long long int powmod(long long int a, long long int b, long long int mo = MOD) {
  long long int res = 1;
  a %= mo;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mo;
    a = a * a % mo;
  }
  return res;
}
inline long long int inv(long long int a) { return powmod(a, MOD - 2, MOD); }
const int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1};
const int dy8[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int dx4[] = {0, 0, 1, -1};
const int dy4[] = {1, -1, 0, 0};
const int N = 111;
double a[N], b;
int n;
vector<double> v;
int main() {
  cin >> n >> b;
  double s = b;
  double p = b;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    s += a[i];
  }
  cout << fixed << setprecision(10);
  double k = s * 1.0 / (n * 1.0);
  int flag = 0;
  for (int i = 1; i <= n; i++) {
    if (a[i] > k + 0.0000001) {
      flag = 1;
    } else {
      v.push_back(k - a[i]);
      p -= k - a[i];
    }
  }
  if (p + 0.0000000001 < 0.0) flag = 1;
  if (flag) {
    cout << -1;
  } else {
    for (auto z : v) cout << z << endl;
  }
}