Problem3174--Ciel and Robot

3174: Ciel and Robot

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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).

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.

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).

Source/Category

 
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