Six distinct numbers are placed on the faces of a die in an arbitrary manner. The die is rolled twice, and after each roll, the sum of the values on the four side faces is calculated. Given these two sums and the set of numbers on the die, determine which numbers could be on the face opposite to the one with the first given number.

Input

The first line contains six distinct positive integers $A_1, \dots, A_6$ separated by spaces, which are the numbers on the faces of the die, each not exceeding $10\,000$.

The second line contains two positive integers separated by a space — the sums of the values on the four side faces of the die resulting from its two rolls. Each sum does not exceed $40\,000$.

Output

In the first and only line, output the values that could be on the face of the die opposite to the face with the value $A_1$, in ascending order. If no such values exist, output $-1$.

Examples

Input 1

2 3 4 5 6 1
13 15

Output 1

4 6