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 math
a, b = [int(i) for i in input().strip().split(" ")]
d = math.gcd(a, b)

divs = []
for i in range(1, int(math.sqrt(d))+1):
    if d % i == 0:
        divs.append(i)
k = len(divs)
divisors = divs[:]
for j in range(1, k+1):
    divisors.append(d//divs[-j])

n=len(divisors)

q = int(input())
for j in range(q):
    low, high = [int(i) for i in input().strip().split(" ")]

    left = 0
    right = n-1
    while left < right:
        mid = left + (right - left)//2
        if divisors[mid] >= low:
            right = mid
        else:
            left = mid + 1
    if divisors[left] < low:
        d1 = -1
    else:
        d1 = divisors[left]

    left = 0
    right = n - 1
    while left < right:
        mid = left + (right - left + 1) // 2
        if divisors[mid] <= high:
            left = mid
        else:
            right = mid - 1
    if divisors[left] > high:
        d2 = -1
    else:
        d2 = divisors[left]

    if d1<0 or d2<0 or d1>d2:
        ans = -1
    else:
        ans = d2
    print(ans)