In a n x m chessboard with cells labeled (*i*, *j*) for 1 ≤ *i* ≤ *N*, 1 ≤ *j* ≤ *M*, there is a stone at (1, 1). A and B is playing a game.

A starts first, and they alternately move stone to adjacent cell (north / west / south / east). It's okay to move stones to previously visited cells, but it's prohibited to move stones to previously visited "edges". For example, if someone wants to move stone from (1, 1) -> (1, 2), they shouldn't have a record of visiting (1, 1) / (1, 2) or (1, 2) / (1, 1) cells consecutively. Player unable to make a move loses.

Who is the winner? 1 ≤ *n*, *m* ≤ 10^{6}

About 1 month ago, me and other guys tried to solve this problem but failed. I also googled about this problem, but wasn't able to find any resources about it :/ Here are some observations to share.

**Hint originally written in statement**

**Observation 1**

**Observation 2**

**Observation 3**

**Observation 4**

Could anyone help me to solve this?