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:
# DON'T USE PYTHON FOR RECURSION
# TRY PYPY
import math
import operator
import sys
import threading
from bisect import bisect_left, bisect
from collections import Counter, defaultdict
from math import ceil, floor, pi, sin, sqrt
from sys import exit, stdin, stdout


def main():
    # stdin = open('.in')
    a, b = map(int, stdin.readline().strip().split(' '))

    def get_divs(n):
        divs = set()
        for i in range(1, int(floor(sqrt(n))) + 1):
            if not n % i:
                divs.add(i)
                divs.add(n / i)
        return divs

    divs = sorted(get_divs(a) & get_divs(b))
    #print divs
    n = int(stdin.readline())
    for _ in range(n):
        l, r = map(int, stdin.readline().strip().split(' '))
        i = bisect(divs, r)
        print divs[i - 1] if divs[i - 1] >= l else -1


if __name__ == '__main__':
    sys.setrecursionlimit(10**6)
    threading.stack_size(10240000)
    thread = threading.Thread(target=main)
    thread.start()