{"raw_statement":[{"iden":"problem statement","content":"We have a rectangular room that is $H$ meters long and $W$ meters wide.  \nWe will cover this room with $A$ indistinguishable $2$ meters $\\times$ $1$ meters rectangular tatami mats and $B$ indistinguishable $1$ meter $\\times$ $1$ meter square tatami mats. The rectangular mats can be used in either direction: they can be $2$ meters long and $1$ meter wide, or $1$ meter long and $2$ meters wide.  \nHow many ways are there to do this?  \nHere, it is guaranteed that $2A + B = HW$, and two ways are distinguished if they match only after rotation, reflection, or both."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 ≤ H, W$\n*   $HW ≤ 16$\n*   $0 ≤ A, B$\n*   $2A + B = HW$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$ $A$ $B$"},{"iden":"sample input 1","content":"2 2 1 2"},{"iden":"sample output 1","content":"4\n\nThere are four ways as follows:\n![image](https://img.atcoder.jp/ghi/d01b63c75c91bd87a73e9a4cc43dda28.png)"},{"iden":"sample input 2","content":"3 3 4 1"},{"iden":"sample output 2","content":"18\n\nThere are six ways as follows, and their rotations.\n![image](https://img.atcoder.jp/ghi/b7a492abe22e30683e8f9a7b309acd52.png)"},{"iden":"sample input 3","content":"4 4 8 0"},{"iden":"sample output 3","content":"36"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}