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:
a,b = map(int,input().split())
arr = []
arr_len = 0
cnt = 0
a,b = min(a,b),max(a,b)
for x in range(1,int(a**.5)+1):
    if a % x == 0:
        arr.append(x)
        arr.append(a//x)
        arr_len += 2
for x in range(arr_len):
    if b % arr[x] != 0:
        arr[x] = -1
        cnt += 1
        arr_len -= 1
arr = list(set(sorted(arr)[cnt:]))
for i in range(int(input())):
    res = -1
    l,r = map(int,input().split())
    for d in arr:
        if d >= l and d <= r:
            res = max(res,d)
    print(res)