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 sys
lines = sys.stdin.readlines()
(m, n) = map(int, lines[0].strip().split(" "))
def gcd(a, b):
        if a == 0: return b
        if a > b: return gcd(b, a)
        return gcd(b%a, a)
G = gcd(m, n)
tmp = G
factors = []
i = 2
while i**2 <= tmp:
    if tmp % i == 0:
        factors.append(i)
        tmp//=i
    else: i += 1
if tmp != 1: factors.append(tmp)
count = {}
for f in factors:
    if f not in count:
        count[f] = 0
    count[f] += 1
primes = list(count.keys())
primes.sort()
factors = [1]
for p in primes:
    tmp = []
    for f in factors:
        for i in range(1, count[p]+1):
            tmp.append(f * p ** i)
    factors += tmp

factors.sort()
L = len(factors)

Q = int(lines[1].strip())
for q in range(2, Q+2):
    (lo, hi) = map(int, lines[q].strip().split(" "))
    l, r = 0, L
    while l < r-1:
        mid = (r-l)//2 + l
        if factors[mid] > hi: r = mid
        else: l = mid
    if factors[l] >= lo: print(factors[l])
    else: print(-1)