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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 .

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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