YSACODE discuss3

A continued fraction of height n is a fraction of form $\text{[math]}$ . You are given two rational numbers, one is represented as $\text{[math]}$ 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,...,a_n (1≤a_i≤10¹⁸) − the continued fraction.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. 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 $\text{[math]}$ .

In the second sample $\text{[math]}$ .

In the third sample $\text{[math]}$ .

3220: Continued Fractions

Description

Source/Category