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 PYTHON3):

Solution:
class CodeforcesTask174ASolution:
    def __init__(self):
        self.result = ''
        self.n_b = []
        self.capacity = []

    def read_input(self):
        self.n_b = [int(x) for x in input().split(" ")]
        self.capacity = [int(x) for x in input().split(" ")]

    def process_task(self):
        mx = max(self.capacity)
        to_fill = sum([mx - x for x in self.capacity])
        if to_fill > self.n_b[1]:
            self.result = "-1"
        else:
            result = []
            for x in self.capacity:
                result.append(mx - x + (self.n_b[1] - to_fill) / self.n_b[0])
            self.result = "\n".join([str(y) for y in result])

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask174ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())