35046번 - Honey Cake 스페셜 저지다국어

문제

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.

입력

The first line of input contains three integers: $w,ドル $h,ドル and $d,ドル the dimensions of the honey cake in inches (1ドル \le w, h, d \le 10^9$).

The second line contains a single integer $n$ (1ドル \le n \le 10^9$).

출력

Output three integers $w_c,ドル $h_c,ドル $d_c,ドル the number of cuts to be made along each of the dimensions $w,ドル $h,ドル and $d,ドル 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.

제한

노트

In the first example, the cake will be cut into 5ドル \cdot 4 \cdot 2 = 40$ pieces of size 2ドル \times 5 \times 3$ inches.