{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\leq N,M \\leq 1000$\n*   $0 \\leq K \\leq NM$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $K$"},{"iden":"sample input 1","content":"2 2 2"},{"iden":"sample output 1","content":"Yes\n\nPress the buttons in the order of the first row, the first column."},{"iden":"sample input 2","content":"2 2 1"},{"iden":"sample output 2","content":"No"},{"iden":"sample input 3","content":"3 5 8"},{"iden":"sample output 3","content":"Yes\n\nPress the buttons in the order of the first column, third column, second row, fifth column."},{"iden":"sample input 4","content":"7 9 20"},{"iden":"sample output 4","content":"No"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}