Triangular Room#643
Many books on recreational mathematics present the following problem: Arrange chairs around the perimeter of a triangular room so that near each wall there are chairs. The solution to this problem is to put one chair in each corner of the room.
Now consider a more general case. Suppose the room is shaped like triangle . The total number of chairs is given, as well as the number of chairs n_{AB} that must be placed near wall , the number of chairs n_{BC} that must be placed near wall , and the number of chairs n_{AC} that must be placed near wall . You are to find the total number of chair arrangements that satisfy these conditions. Chairs may be placed only at the corners of the room and along the walls—placing chairs in the center is not allowed. Any number of chairs may be placed at each corner.
The input file contains the integers , n_{AB}, n_{BC}, n_{AC} (0 \leq n, n_{AB}, n_{BC}, n_{AC} \leq 10^{18}).
Print the number of possible arrangements in the first line of the output file. If there is at least one arrangement, print on the second line non-negative integers: k_A, k_{AB}, k_B, k_{BC}, k_C, k_{AC}—the number of chairs to be placed respectively at corner , along wall , at corner , along wall , at corner , and along wall .
Example 1