Codeforces Beta Round #67 (Div. 2)C. Modified GCD-优快云博客

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

output

3
-1
9

题目大意：找出a b的公因子然后给几个查询，查询在x y之间的最大公因子输出。

先把因子找出来，然后二分找一下最大的.

其实找因子一共有两种方法（就我所知）对于10^18这种级别的用质因子那种方法找，对于10^9这种级别的用sqrt(n)的方法枚举因子的方法去找.....

/* ***********************************************
Author        :guanjun
Created Time  :2016/10/30 10:11:46
File Name     :cf67c.cpp
************************************************ */
#include <bits/stdc++.h>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 0x3f3f3f3f
#define maxn 10010
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
using namespace std;
priority_queue<int,vector<int>,greater<int> >pq;
struct Node{
    int x,y;
};
struct cmp{
    bool operator()(Node a,Node b){
        if(a.x==b.x) return a.y> b.y;
        return a.x>b.x;
    }
};

bool cmp(int a,int b){
    return a>b;
}
vector<int>v;
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
    int a,b,x,y,n;
    cin>>a>>b;
    a=__gcd(a,b);
    b=sqrt(a);
    v.clear();
    for(int i=1;i<=b;i++){
        if(a%i==0){
            if(i*i==a)v.push_back(i);
            else v.push_back(i),v.push_back(a/i);
        }
    }
    sort(v.begin(),v.end());

    cin>>n;
    for(int i=1;i<=n;i++){
        cin>>x>>y;
        int pos=upper_bound(v.begin(),v.end(),y)-v.begin()-1;
        if(x>v[pos])puts("-1");
        else cout<<v[pos]<<endl;
    }
    return 0;
}