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F. New Year and Cleaning

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLimak 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.

Input

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'.

Output

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.

Examples

Input

1 10 2

R

Output

30

Input

3 4 6

RUL

Output

134

Input

4 1 500000

RLRL

Output

-1

Note

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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