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):
    if(b == 0):
        return a
    return gcd(b, a % b)
from bisect import bisect_right as br
def main():
    a, b = [int(i) for i in input().split()]
    d = gcd(a, b)
    q = int(input())
    k = 2
    p = [1, d]
    while(k*k <= d):
        if(d % k == 0):
            p += [k]
            p += [d // k]
        k += 1
    p = sorted(p) + [10**9 + 1]
    for i in range(q):
        l, r = [int(i) for i in input().split()]
        x2 = br(p, r)
        x1 = x2 - 1
        if(p[x2] != 10**9 + 1 and l <= p[x2] <= r):
            print(p[x2])
        elif(x1 != -1 and l <= p[x1] <= r):
            print(p[x1])
        else:
            print(-1)
main()