Ciel and Robot

1000ms

262144K

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).

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.

Sample Input:

2 2
RU

Sample Output:

Yes

Sample Input:

1 2
RU

Sample Output:

No

Sample Input:

-1 1000000000
LRRLU

Sample Output:

Yes

Sample Input:

0 0
D

Sample 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).

Informação

Provedor Codeforces

Código CF321A