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 math

a, b = map(int, input().split())
g = math.gcd(a, b)
di = []

i = 1

while (i * i <= g):
    if (g % i == 0):
        di.append(i)
        if (i * i != g): di.append(g // i)
    
    i += 1
    
di.sort()
m = len(di)

q = int(input())

for i in range(q):
    x, y = map(int, input().split())
    l, r, p = 0, m - 1, 0
    
    while (l <= r):
        mid = (l + r) // 2
        
        if (di[mid] <= y):
            p, l = mid, mid + 1
        else:
            r = mid - 1
            
    if (di[p] >= x):
        print(di[p])
    else:
        print(-1)