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:

def gcd(a,b):
	if b == 0 : 
		return a
	else:
		return gcd(b , a % b)

(a,b) = map(int,raw_input().split())

g = gcd(a,b)

a = []
b = []
c = []

i = 1;
while i * i <= g:
	if g % i == 0:
		a.append(i)
		if(i != g / i):
			b.append(g / i)
	i += 1

for i in range(len(b) - 1, -1,-1):
	a.append(b[i])

q = input()


for i in range (q):

	(c,d) = map(int,raw_input().split())

	low = 0;high = len(a) - 1 ; res = -1

	while low <= high :
		mid = (low + high) / 2
		if a[mid] <= d :
			res = mid
			low = mid + 1
		else:
			high = mid - 1

	if res == -1 or a[res] < c:
		print -1
	else:
		print a[res]