{"raw_statement":[{"iden":"problem statement","content":"There is a bar of chocolate with a height of $H$ blocks and a width of $W$ blocks. Snuke is dividing this bar into exactly three pieces. He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.\nSnuke is trying to divide the bar as evenly as possible. More specifically, he is trying to minimize $S_{max}$ - $S_{min}$, where $S_{max}$ is the area (the number of blocks contained) of the largest piece, and $S_{min}$ is the area of the smallest piece. Find the minimum possible value of $S_{max} - S_{min}$."},{"iden":"constraints","content":"*   $2 ≤ H, W ≤ 10^5$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$"},{"iden":"sample input 1","content":"3 5"},{"iden":"sample output 1","content":"0\n\nIn the division below, $S_{max} - S_{min} = 5 - 5 = 0$.\n\n![image](https://atcoder.jp/img/arc074/2a9b2ef47b750c0b7ba3e865d4fb4203.png)"},{"iden":"sample input 2","content":"4 5"},{"iden":"sample output 2","content":"2\n\nIn the division below, $S_{max} - S_{min} = 8 - 6 = 2$.\n\n![image](https://atcoder.jp/img/arc074/a42aae7aaaadc4640ac5cdf88684d913.png)"},{"iden":"sample input 3","content":"5 5"},{"iden":"sample output 3","content":"4\n\nIn the division below, $S_{max} - S_{min} = 10 - 6 = 4$.\n\n![image](https://atcoder.jp/img/arc074/eb0ad0cb3185b7ae418e21c472ff7f26.png)"},{"iden":"sample input 4","content":"100000 2"},{"iden":"sample output 4","content":"1"},{"iden":"sample input 5","content":"100000 100000"},{"iden":"sample output 5","content":"50000"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}