The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 184 (Div. 2) |
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Finished |

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brute force

implementation

math

*1700

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B. Continued Fractions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA continued fraction of height *n* is a fraction of form . You are given two rational numbers, one is represented as 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* ≤ 10^{18}) — 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 *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{18}) — 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 .

In the second sample .

In the third sample .

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