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 PYTHON3):

Solution:
def gcd(a,b):
    while a>0:
        x=a
        a=b%a
        b=x
    return(x)
def Bsearch1(L,x):
    beg=0
    last=len(L)-1
    while beg<=last:
        mid=(beg+last)//2
        if x==L[mid]:
            return(mid)
        elif(x>L[mid]):
            beg=mid+1
        else:
            last=mid-1
    else:
        return(beg)
def Bsearch2(L,x):
    beg=0
    last=len(L)-1
    while beg<=last:
        mid=(beg+last)//2
        if x==L[mid]:
            return(mid)
        elif(x>L[mid]):
            beg=mid+1
        else:
            last=mid-1
    else:
        return(last)
a,b=input().split()
a,b=[int(a),int(b)]
x=gcd(a,b)
from functools import reduce
def factors(n):
    x=set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
    return(list(x))
div=factors(x)
div.sort()
y=int(input())
for j in range(y):
    c,d=input().split()
    c,d=[int(c),int(d)]
    f=Bsearch1(div,c)
    g=Bsearch2(div,d)
    if f>g:
        print(-1)
    else:
        print(div[g])