#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<cmath>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<vector>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

const int inf=1e9+5;
const int maxn=1e8+7;
const int mod=1e9+7;
const double eps=1e-8;
const double pi=acos(-1.0);

ll gcd(ll a,ll b){ return b==0?a:gcd(b,a%b); }