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:
#!/usr/bin/python

import sys
import math

def gcd(x, y):
    if x < y:
        x,y = y,x
    if x % y == 0:
        return y
    return gcd(y, x % y)

if __name__=="__main__":
    data = sys.stdin.readlines()
    a,b = [int(v) for v in data[0].split(' ')]
    v = gcd(a,b)
    li = []
    for i in range(1,int(math.sqrt(v))+2):
        if v % i == 0:
            if v / i < i:
                break
            elif v / i == i:
                li.append(i)
                break
            else:
                li += [i,v/i]
    li.sort()
    n = int(data[1])
    for i in range(0,n):
        low, high = [int(v) for v in data[i+2].split(' ')]
        ans = -1
        b, e = 0,len(li)-1
        while b <= e:
            m = (b + e) / 2
            if li[m] < low:
                b = m + 1
            elif li[m] > high:
                e = m - 1
            else:
                ans = max(ans, li[m])
                b = m + 1
        print ans