A. Ciel and Robottime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard 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).InputThe 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.OutputPrint "Yes" if the robot will be located at (a, b), and "No" otherwise.ExamplesInput2 2RUOutputYesInput1 2RUOutputNoInput-1 1000000000LRRLUOutputYesInput0 0DOutputYesNoteIn 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).
Input2 2RU
OutputYes
['binary search', 'implementation', 'math', '*1700']