Hannah and Henry are going to host a party for (n) people, including themselves. They bought a honey cake of size (w \times h \times d) inches for the party, and want to split it into (n) equal pieces. The honey cake can be cut parallel to any of its faces. To make cuts precise, each edge of length (w) is cut into the same number of equal parts, each having integer length; similarly for edges of lengths (h) and (d). Given the dimensions of the honey cake, determine whether it is possible to cut it into (n) equal pieces, and if so, how. The first line of input contains three integers: (w), (h), and (d), the dimensions of the honey cake in inches ((1 \le w, h, d \le 10^9)). The second line contains a single integer (n) ((1 \le n \le 10^9)). Output three integers (w_c), (h_c), (d_c), the number of cuts to be made along each of the dimensions (w), (h), and (d), respectively, if it is possible to cut the cake, or a single integer (-1) otherwise. Note that making zero cuts along a dimension is allowed, too. In the first example, the cake will be cut into (5 \cdot 4 \cdot 2 = 40) pieces of size (2 \times 5 \times 3) inches.