799_D. Field expansion
In one of the games Arkady is fond of the game process happens on a rectangular field. In the game process Arkady can buy extensions for his field, each extension enlarges one of the field sizes in a particular number of times. Formally, there are n extensions, the i-th of them multiplies the width or the length (by Arkady's choice) by ai. Each extension can't be used more than once, the extensions can be used in any order.

Now Arkady's field has size h × w. He wants to enlarge it so that it is possible to place a rectangle of size a × b on it (along the width or along the length, with sides parallel to the field sides). Find the minimum number of extensions needed to reach Arkady's goal.

Input

The first line contains five integers a, b, h, w and n (1 ≤ a, b, h, w, n ≤ 100 000) — the sizes of the rectangle needed to be placed, the initial sizes of the field and the number of available extensions.

The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 100 000), where ai equals the integer a side multiplies by when the i-th extension is applied.

Output

Print the minimum number of extensions needed to reach Arkady's goal. If it is not possible to place the rectangle on the field with all extensions, print -1. If the rectangle can be placed on the initial field, print 0.

Examples

Input

3 3 2 4 4
2 5 4 10


Output

1


Input

3 3 3 3 5
2 3 5 4 2


Output

0


Input

5 5 1 2 3
2 2 3


Output

-1


Input

3 4 1 1 3
2 3 2


Output

3

Note

In the first example it is enough to use any of the extensions available. For example, we can enlarge h in 5 times using the second extension. Then h becomes equal 10 and it is now possible to place the rectangle on the field.
```python
def mp():  return map(int,input().split())
def lt():  return list(map(int,input().split()))
def pt(x):  print(x)
def ip():  return input()
def it():  return int(input())
def sl(x):  return [t for t in x]
def spl(x): return x.split()
def aj(liste, item): liste.append(item)
def bin(x):  return "{0:b}".format(x)
def listring(l): return ' '.join([str(x) for x in l])
def ptlist(l): print(' '.join([str(x) for x in l]))
from copy import deepcopy
c,b,h,w,n = mp() 
d = lt()
d.sort(reverse = True)
k = min(n,34)
a = d[:k] 
if (c <= h and b <= w) or (c <= w and b <= h):
    pt(0)
else:
    dict = {h:w}
    i = 0
    bl = True
    while bl and i < k:
        x = a[i]
        dict1 = {}
        for r in dict:
            if r*x in dict1:
                dict1[r*x] = max(dict1[r*x],dict[r])
            else:
                dict1[r*x] = dict[r]
            if r in dict1:
                dict1[r] = max(dict1[r],dict[r]*x)
            else:
                dict1[r] = dict[r]*x
        if any((r>=c and dict1[r]>=b) or (r>=b and dict1[r]>=c) for r in dict1):
            bl = False
        else:
            i += 1
            dict = deepcopy(dict1)
    if i == k:
        pt(-1)
    else:
        pt(i+1)
        
    
            
        
    

```