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:
import bisect

def nod(a,b):
    while True:
        if a>b:
            if a%b==0: return b
            a%=b
        else:
            if b%a==0: return a
            b%=a
a,b=map(int,input().split())
d=nod(a,b)
ds=[]
for i in range(1,int(d**0.5)+1):
    if d%i==0:
        ds.append(i)
        ds.append(d//i)
ds=sorted(list(set(ds))) 
for _ in range(int(input())):
    L,R=map(int,input().split())
    x=bisect.bisect(ds,R)-1
    if ds[x]<L:
        print(-1)
    else:
        print(ds[x])