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 sys
input = sys.stdin.readline
from math import *
def bs(a,x,y):
    l=0
    r=len(a)-1
    ans=-1
    while l<=r:
        mid=l+(r-l)//2
        if x<=a[mid]<=y:
            ans=a[mid]
            l=mid+1
        elif a[mid]>y:
            r=mid-1
        else:
            l=mid+1
    return ans        
a,b = map(int,input().split())
div=[]
g=gcd(a,b)
for i in range(1,int(sqrt(g))+1):
    if g%i==0:
        div.append(i)
        if g//i!=i:
            div.append(g//i)
div.sort()
#print(div)
q=int(input())
for j in range(q):
    x,y=map(int,input().split())
    ans=bs(div,x,y)
    
    if x<=ans<=y:
        print(ans)
    else:
        print(-1)