Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Ciel and Robot

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFox Ciel has a robot on a 2D plane. Initially it is located in (0, 0). Fox Ciel code a command to it. The command was represented by string *s*. Each character of *s* is one move operation. There are four move operations at all:

- 'U': go up, (x, y) → (x, y+1);
- 'D': go down, (x, y) → (x, y-1);
- 'L': go left, (x, y) → (x-1, y);
- 'R': go right, (x, y) → (x+1, y).

The robot will do the operations in *s* from left to right, and repeat it infinite times. Help Fox Ciel to determine if after some steps the robot will located in (*a*, *b*).

Input

The first line contains two integers *a* and *b*, ( - 10^{9} ≤ *a*, *b* ≤ 10^{9}). The second line contains a string *s* (1 ≤ |*s*| ≤ 100, *s* only contains characters 'U', 'D', 'L', 'R') — the command.

Output

Print "Yes" if the robot will be located at (*a*, *b*), and "No" otherwise.

Examples

Input

2 2

RU

Output

Yes

Input

1 2

RU

Output

No

Input

-1 1000000000

LRRLU

Output

Yes

Input

0 0

D

Output

Yes

Note

In the first and second test case, command string is "RU", so the robot will go right, then go up, then right, and then up and so on.

The locations of its moves are (0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → ...

So it can reach (2, 2) but not (1, 2).

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/22/2019 02:07:12 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|