Continued Fractions

Description:

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, ..., a_n (1 ≤ a_i ≤ 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.

Sample Input:

9 4
2
2 4

Sample Output:

YES

Sample Input:

9 4
3
2 3 1

Sample Output:

YES

Sample Input:

9 4
3
1 2 4

Sample Output:

NO

Note:

In the first sample .

In the second sample .

In the third sample .