#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
long long int MOD = 1000000007;
long long int powmod(long long int a, long long int b) {
  long long int res = 1;
  a %= 1000000009;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % 1000000009;
    a = a * a % 1000000009;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
long long int add(long long int a, long long int b) {
  return ((a % MOD) + (b % MOD)) % MOD;
}
long long int mul(long long int a, long long int b) {
  return ((a % MOD) * (b % MOD)) % MOD;
}
long long int sub(long long int a, long long int b) {
  return ((a % MOD) - (b % MOD) + MOD) % MOD;
}
long long int binpow(long long int x, long long int y) {
  long long int z = 1;
  while (y) {
    if (y & 1) z = mul(z, x);
    x = mul(x, x);
    y >>= 1;
  }
  return z;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  vector<pair<long long int, long long int>> states;
  long long int a, b;
  cin >> a >> b;
  bool ok = false;
  string dir;
  cin >> dir;
  int x = 0;
  int y = 0;
  states.push_back({x, y});
  long long int n = dir.size();
  for (long long int i = 0; i < n; i++) {
    char d = dir[i];
    switch (d) {
      case 'R':
        x++;
        break;
      case 'L':
        x--;
        break;
      case 'U':
        y++;
        break;
      case 'D':
        y--;
        break;
    }
    states.push_back({x, y});
  }
  if (a == 0 && b == 0) {
    cout << "Yes";
    return 0;
  }
  pair<long long int, long long int> need = states[n];
  for (long long int i = 0; i < n + 1; i++) {
    long long int remx = a - states[i].first;
    long long int remy = b - states[i].second;
    long long int sick = remx * need.first;
    long long int kick = remy * need.second;
    if (need.first == 0 && need.second != 0) {
      long long int deb = remy / need.second;
      deb *= need.second;
      if (deb == remy && remx == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else if (need.first != 0 && need.second == 0) {
      long long int deb = remx / need.first;
      deb *= need.first;
      if (remx == deb && remy == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else if (need.first == 0 && need.second == 0) {
      if (remy == 0 && remx == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else {
      if (remx % need.first == 0 && remy % need.second == 0) {
        long long int deb = remy / need.second;
        long long int cheb = remx / need.first;
        if (deb == cheb && sick >= 0 && kick >= 0) {
          ok = true;
        }
      }
    }
  }
  if (ok) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
long long int MOD = 1000000007;
long long int powmod(long long int a, long long int b) {
  long long int res = 1;
  a %= 1000000009;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % 1000000009;
    a = a * a % 1000000009;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
long long int add(long long int a, long long int b) {
  return ((a % MOD) + (b % MOD)) % MOD;
}
long long int mul(long long int a, long long int b) {
  return ((a % MOD) * (b % MOD)) % MOD;
}
long long int sub(long long int a, long long int b) {
  return ((a % MOD) - (b % MOD) + MOD) % MOD;
}
long long int binpow(long long int x, long long int y) {
  long long int z = 1;
  while (y) {
    if (y & 1) z = mul(z, x);
    x = mul(x, x);
    y >>= 1;
  }
  return z;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  vector<pair<long long int, long long int>> states;
  long long int a, b;
  cin >> a >> b;
  bool ok = false;
  string dir;
  cin >> dir;
  int x = 0;
  int y = 0;
  states.push_back({x, y});
  long long int n = dir.size();
  for (long long int i = 0; i < n; i++) {
    char d = dir[i];
    switch (d) {
      case 'R':
        x++;
        break;
      case 'L':
        x--;
        break;
      case 'U':
        y++;
        break;
      case 'D':
        y--;
        break;
    }
    states.push_back({x, y});
  }
  if (a == 0 && b == 0) {
    cout << "Yes";
    return 0;
  }
  pair<long long int, long long int> need = states[n];
  for (long long int i = 0; i < n + 1; i++) {
    long long int remx = a - states[i].first;
    long long int remy = b - states[i].second;
    long long int sick = remx * need.first;
    long long int kick = remy * need.second;
    if (need.first == 0 && need.second != 0) {
      long long int deb = remy / need.second;
      deb *= need.second;
      if (deb == remy && remx == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else if (need.first != 0 && need.second == 0) {
      long long int deb = remx / need.first;
      deb *= need.first;
      if (remx == deb && remy == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else if (need.first == 0 && need.second == 0) {
      if (remy == 0 && remx == 0 && sick >= 0 && kick >= 0) {
        ok = true;
      }
    } else {
      if (remx % need.first == 0 && remy % need.second == 0) {
        long long int deb = remy / need.second;
        long long int cheb = remx / need.first;
        if (deb == cheb && sick >= 0 && kick >= 0) {
          ok = true;
        }
      }
    }
  }
  if (ok) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
}

```