#P321A. Ciel and Robot

    ID: 2719 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>binary searchimplementationmath*1700

Ciel and Robot

No submission language available for this problem.

Description

Fox 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).

The first line contains two integers a and b, ( - 109 ≤ a, b ≤ 109). The second line contains a string s (1 ≤ |s| ≤ 100, s only contains characters 'U', 'D', 'L', 'R') — the command.

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

Input

The first line contains two integers a and b, ( - 109 ≤ a, b ≤ 109). 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.

Samples

2 2
RU

Yes

1 2
RU

No

-1 1000000000
LRRLU

Yes

0 0
D

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).