Problem: Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.

A common divisor for two positive numbers is a number which both numbers are divisible by.

But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low ≤ d ≤ high. It is possible that there is no common divisor in the given range.

You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.

Input

The first line contains two integers a and b, the two integers as described above (1 ≤ a, b ≤ 109). The second line contains one integer n, the number of queries (1 ≤ n ≤ 104). Then n lines follow, each line contains one query consisting of two integers, low and high (1 ≤ low ≤ high ≤ 109).

Output

Print n lines. The i-th of them should contain the result of the i-th query in the input. If there is no common divisor in the given range for any query, you should print -1 as a result for this query.

Examples

Input

9 27
3
1 5
10 11
9 11


Output

3
-1
9

Solution (in PYTHON):

Solution:
from math import sqrt
def bsearch(lo,hi,b):
    if lo>hi:
        return lo
    mid=(lo+hi)/2
    mid=int(mid)
    #print 'mid=',mid
    if arr[mid]==b:
        return mid
    elif arr[mid]>b:
        return bsearch(lo,mid-1,b)
    else:
        return bsearch(mid+1,hi,b)
def gcd(a,b):
    if b:
        return gcd(b,a%b)
    else:
        return a
a,b=map(int,raw_input().split())
g=gcd(a,b)
alist=[]
blist=[]
for i in xrange(1,int(sqrt(g)+1)):
    if g%i==0:
        alist.append(i)
        blist.append(g/i)
arr=alist
for i in reversed(blist):
    arr.append(i)
#print arr
l=len(arr)
c=input()
while c:
    flag=1
    m,n=map(int,raw_input().split())
    if arr[l-1]<m:
        print -1
    else:
        i=bsearch(0,l-1,n)
        while i>l-1:
            i-=1
        while m<=arr[i] and i>=0:
            if arr[i]<=n:
                print arr[i]
                flag=0
                break
            else:
                i-=1
        if flag:
            print '-1'
    c-=1