Limak is a little polar bear. His parents told him to clean a house before the New Year's Eve. Their house is a rectangular grid with h rows and w columns. Each cell is an empty square. He is a little bear and thus he can't clean a house by himself. Instead, he is going to use a cleaning robot. A cleaning robot has a built-in pattern of n moves, defined by a string of the length n . A single move (character) moves a robot to one of four adjacent cells. Each character is one of the following four: ' U ' (up), ' D ' (down), ' L ' (left), ' R ' (right). One move takes one minute. A cleaning robot must be placed and started in some cell. Then it repeats its pattern of moves till it hits a wall (one of four borders of a house). After hitting a wall it can be placed and used again. Limak isn't sure if placing a cleaning robot in one cell will be enough. Thus, he is going to start it w · h times, one time in each cell. Maybe some cells will be cleaned more than once but who cares? Limak asks you one question. How much time will it take to clean a house? Find and print the number of minutes modulo 10 9 + 7 . It's also possible that a cleaning robot will never stop — then print " -1 " (without the quotes) instead. Placing and starting a robot takes no time, however, you must count a move when robot hits a wall. Take a look into samples for further clarification. The first line contains three integers n , h and w ( 1 ≤ n , h , w ≤ 500 000 ) — the length of the pattern, the number of rows and the number of columns, respectively. The second line contains a string of length n — the pattern of n moves. Each character is one of uppercase letters ' U ', ' D ', ' L ' or ' R '. Print one line with the answer. If a cleaning robot will never stop, print " -1 " (without the quotes). Otherwise, print the number of minutes it will take to clean a house modulo 10 9 + 7 . In the first sample house is a grid with 10 rows and 2 columns. Starting a robot anywhere in the second column