#include <bits/stdc++.h>
const double eps = (1e-10);
using namespace std;
int dcmp(long double a, long double b) {
  return fabsl(a - b) <= eps ? 0 : (a > b) ? 1 : -1;
}
int getBit(int num, int idx) { return ((num >> idx) & 1) == 1; }
int setBit1(int num, int idx) { return num | (1 << idx); }
long long setBit0(long long num, int idx) { return num & ~(1ll << idx); }
long long flipBit(long long num, int idx) { return num ^ (1ll << idx); }
void M() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int countNumBit1(int mask) {
  int ret = 0;
  while (mask) {
    mask &= (mask - 1);
    ++ret;
  }
  return ret;
}
long long X, Y, x, y, fl;
string st;
long long sx, sy, GX, GY;
int getquad(long long GX, long long GY) {
  int fl;
  if (GX >= 0 && GY >= 0)
    fl = 1;
  else if (GX <= 0 && GY >= 0)
    fl = 2;
  else if (GX <= 0 && GY <= 0)
    fl = 3;
  else
    fl = 4;
  return fl;
}
int main() {
  cin >> x >> y >> st;
  if (x == 0 && y == 0) {
    cout << "Yes\n";
    return 0;
  }
  GX = 0, GY = 0;
  for (int i = 0; i < ((int)(st).size()); i++) {
    if (st[i] == 'U') GY += 1;
    if (st[i] == 'R') GX += 1;
    if (st[i] == 'L') GX -= 1;
    if (st[i] == 'D') GY -= 1;
  }
  if (GX >= 0 && GY >= 0)
    fl = 1;
  else if (GX <= 0 && GY >= 0)
    fl = 2;
  else if (GX <= 0 && GY <= 0)
    fl = 3;
  else
    fl = 4;
  X = 0, Y = 0;
  for (int i = 0; i < ((int)(st).size()); i++) {
    if (st[i] == 'U') Y += 1;
    if (st[i] == 'R') X += 1;
    if (st[i] == 'L') X -= 1;
    if (st[i] == 'D') Y -= 1;
    sx = x - X;
    sy = y - Y;
    if (sx == 0 && sy == 0) {
      cout << "Yes\n";
      return 0;
    }
    if (getquad(sx, sy) != fl) continue;
    bool ok1 = (GX == 0 ? sx == 0 : sx % GX == 0);
    bool ok2 = (GY == 0 ? sy == 0 : sy % GY == 0);
    if (ok1 && ok2 && sx * GY == GX * sy) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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).

### Response

```cpp
#include <bits/stdc++.h>
const double eps = (1e-10);
using namespace std;
int dcmp(long double a, long double b) {
  return fabsl(a - b) <= eps ? 0 : (a > b) ? 1 : -1;
}
int getBit(int num, int idx) { return ((num >> idx) & 1) == 1; }
int setBit1(int num, int idx) { return num | (1 << idx); }
long long setBit0(long long num, int idx) { return num & ~(1ll << idx); }
long long flipBit(long long num, int idx) { return num ^ (1ll << idx); }
void M() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int countNumBit1(int mask) {
  int ret = 0;
  while (mask) {
    mask &= (mask - 1);
    ++ret;
  }
  return ret;
}
long long X, Y, x, y, fl;
string st;
long long sx, sy, GX, GY;
int getquad(long long GX, long long GY) {
  int fl;
  if (GX >= 0 && GY >= 0)
    fl = 1;
  else if (GX <= 0 && GY >= 0)
    fl = 2;
  else if (GX <= 0 && GY <= 0)
    fl = 3;
  else
    fl = 4;
  return fl;
}
int main() {
  cin >> x >> y >> st;
  if (x == 0 && y == 0) {
    cout << "Yes\n";
    return 0;
  }
  GX = 0, GY = 0;
  for (int i = 0; i < ((int)(st).size()); i++) {
    if (st[i] == 'U') GY += 1;
    if (st[i] == 'R') GX += 1;
    if (st[i] == 'L') GX -= 1;
    if (st[i] == 'D') GY -= 1;
  }
  if (GX >= 0 && GY >= 0)
    fl = 1;
  else if (GX <= 0 && GY >= 0)
    fl = 2;
  else if (GX <= 0 && GY <= 0)
    fl = 3;
  else
    fl = 4;
  X = 0, Y = 0;
  for (int i = 0; i < ((int)(st).size()); i++) {
    if (st[i] == 'U') Y += 1;
    if (st[i] == 'R') X += 1;
    if (st[i] == 'L') X -= 1;
    if (st[i] == 'D') Y -= 1;
    sx = x - X;
    sy = y - Y;
    if (sx == 0 && sy == 0) {
      cout << "Yes\n";
      return 0;
    }
    if (getquad(sx, sy) != fl) continue;
    bool ok1 = (GX == 0 ? sx == 0 : sx % GX == 0);
    bool ok2 = (GY == 0 ? sy == 0 : sy % GY == 0);
    if (ok1 && ok2 && sx * GY == GX * sy) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
}

```