{"problem":{"name":"fLIP","description":{"content":"We have a grid with $N$ rows and $M$ columns of squares. Initially, all the squares are white. There is a button attached to each row and each column. When a button attached to a row is pressed, the c","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"code_festival_2017_quala_b"},"statements":[{"statement_type":"Markdown","content":"We have a grid with $N$ rows and $M$ columns of squares. Initially, all the squares are white.\nThere is a button attached to each row and each column. When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa. When a button attached to a column is pressed, the colors of all the squares in that column are inverted.\nTakahashi can freely press the buttons any number of times. Determine whether he can have exactly $K$ black squares in the grid.\n\n## Constraints\n\n*   $1 \\leq N,M \\leq 1000$\n*   $0 \\leq K \\leq NM$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"code_festival_2017_quala_b","tags":[],"sample_group":[["2 2 2","Yes\n\nPress the buttons in the order of the first row, the first column."],["2 2 1","No"],["3 5 8","Yes\n\nPress the buttons in the order of the first column, third column, second row, fifth column."],["7 9 20","No"]],"created_at":"2026-03-03 11:01:14"}}