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:
from math import sqrt
def bin_ser(co_szuk):
    start, koniec = 0, len(dzielniki) - 1
    while start < koniec:
        srodek = (koniec + start + 1) // 2
        if dzielniki[srodek] > co_szuk:
            koniec = srodek - 1
        else:
            start = srodek
    return dzielniki[start]
def nwd(a, b):
    while b:
        a, b = b, a % b
    return a
a, b = map(int, input().split())
NWD = nwd(a,b)
dzielniki = []
for i in range(1, int(sqrt(NWD)) + 1):
    if NWD % i == 0:
        dzielniki.append(i)
        if i * i != NWD:
            dzielniki.append(NWD // i)
dzielniki.sort()
for t in range(int(input())):
    low, high = map(int, input().split())
    wynik = bin_ser(high)
    if wynik <= high and wynik >= low:
        print(wynik)
    else:
        print(-1)