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
import math
from collections import defaultdict
import bisect
def alele(): return list(map(int, sys.stdin.readline().strip().split()))
def ilele(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 1000000000 + 7

def printDivisors(n) : 
    A=[] 
    i = 1
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n / i == i) : 
                A.append(i) 
            else : 
                A.append(i) 
                A.append(n//i) 
        i = i + 1
    return A

a,b = ilele()
c =min(a,b);d = max(a,b)
A = printDivisors(c)
B = []
for i in A:
    if d%i == 0:
        B.append(i)
B.sort()
#print(B)
for _ in range(int(input())):
    a,b= ilele()
    x = bisect.bisect_left(B,b)
    if x<len(B) and B[x] == b:
        print(b)
    elif x==0:
        print(-1)
    elif B[x-1] >= a:
        print(B[x-1])
    else:
        print(-1)