cf 305B

F - Continued Fractions

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit Status Practice CodeForces 305B

Appoint description:  System Crawler  (2015-01-10)

Description

A 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 ≤ 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 integersa₁, 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 %I64dspecifier.

Output

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

Sample Input

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

Hint

In the first sample .

In the second sample .

In the third sample .

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<string>
#include<cmath>
#include<algorithm>
#include<queue>
#include<set>
#include<vector>
using namespace std;
#define LL long long
LL n,a[110],p,q;
int main()
{
      bool flag=false;
      cin>>p>>q>>n;
      for(int i=0;i<n;i++)
            cin>>a[i];
      for(int i=0;i<n;i++)
      {
            double res=(double)(p)/q-a[i];
            if(!res&&i==n-1)
            {
                  printf("YES\n");
                  flag=true;
            }
            else if(res>0&&res<=1)
            {
                  p=p-q*a[i];
                  LL temp=p;
                  p=q;
                  q=temp;
            }
            else
            {
                 flag=true;
                 printf("NO\n");
                 break;
            }
      }
      if(!flag)
            printf("NO\n");
      return 0;
}