#include <bits/stdc++.h>
using namespace std;
long long a, b, p, q;
vector<long long> v, v1;
long long n, t;
long long good() {
  if (v.size() != v1.size()) return false;
  for (int i = 0; i < v.size(); i++)
    if (v[i] != v1[i]) return false;
  return true;
}
void solve(long long a, long long b) {
  if (a == 0 || b == 0) return;
  v1.push_back(a / b);
  a %= b;
  solve(b, a);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> p >> q;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> t;
    v.push_back(t);
  }
  if (v.size() > 1 && v[n - 1] == 1) {
    v.erase(v.end() - 1);
    --n;
    v[n - 1]++;
  }
  solve(p, q);
  if (good())
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  cin.get();
  cin.get();
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

A continued fraction of height n is a fraction of form <image>. You are given two rational numbers, one is represented as <image> and the other one is represented as a finite fraction of height n. Check if they are equal.

Input

The first line contains two space-separated integers p, q (1 ≤ q ≤ p ≤ 1018) — the numerator and the denominator of the first fraction.

The second line contains integer n (1 ≤ n ≤ 90) — the height of the second fraction. The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1018) — the continued fraction.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print "YES" if these fractions are equal and "NO" otherwise.

Examples

Input

9 4
2
2 4


Output

YES


Input

9 4
3
2 3 1


Output

YES


Input

9 4
3
1 2 4


Output

NO

Note

In the first sample <image>.

In the second sample <image>.

In the third sample <image>.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long a, b, p, q;
vector<long long> v, v1;
long long n, t;
long long good() {
  if (v.size() != v1.size()) return false;
  for (int i = 0; i < v.size(); i++)
    if (v[i] != v1[i]) return false;
  return true;
}
void solve(long long a, long long b) {
  if (a == 0 || b == 0) return;
  v1.push_back(a / b);
  a %= b;
  solve(b, a);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> p >> q;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> t;
    v.push_back(t);
  }
  if (v.size() > 1 && v[n - 1] == 1) {
    v.erase(v.end() - 1);
    --n;
    v[n - 1]++;
  }
  solve(p, q);
  if (good())
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  cin.get();
  cin.get();
  return 0;
}

```