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 *
def nwd(a, b):
    while b!=0:
        c = a%b
        a = b
        b = c
    return a

def binSearch(h):
    p = 0
    k = len(dzielniki)-1
    while(p<k):
        s = int((p+k+1)/2)
        if dzielniki[s] > h:
            k = s-1
        else:
            p = s
    return dzielniki[p]



a, b = map(int, input().split())
najwyzszy_dzielnik = nwd(a,b)
dzielniki = []
pierwiastek = int(sqrt(najwyzszy_dzielnik))
#GENEROWANIE WSPOLNYCH DZIELNIKÓW
for i in range(1, pierwiastek+1):
    if najwyzszy_dzielnik%i == 0:
        dzielniki.append(i)
        dzielniki.append(int(najwyzszy_dzielnik/i))
        if i*i == najwyzszy_dzielnik:
            dzielniki.pop()
dzielniki.sort()
t = int(input())
for i in range(t):
    low, high = map(int, input().split())
    wynik = binSearch(high)
    if wynik <= high and wynik >= low:
        print(wynik)
    else:
        print(-1)