CF611F.New Year and Cleaning

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 $w$ ( $1<=n,h,w<=500000$ ) — 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 will result in only one move (thus, one minute of cleaning) in which robot will hit a wall — he tried to go right but there is no third column. Starting a robot anywhere in the first column will result in two moves. The total number of minutes is $10·1+10·2=30$ .

In the second sample a started robot will try to move "RULRULRULR..." For example, for the leftmost cell in the second row robot will make $5$ moves before it stops because of hitting an upper wall.