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/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
long factorial(int n)
{
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
long factorial(int n)
{
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
bitset<10000010>bs;
vector<int>primes; //Stores tall the primes to n
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
#define M 1000000
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include <bits/stdc++.h>
using namespace std;
#define MAX 500010
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
bool isPrime (int n)
{
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
void ConvertBase(int N,int base)
{
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
//Big Mod
int big_mod(int base, int power, int mod)
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
//1. Brute Force
int modInverse(int a, int m)
/* Bismillah hir rahmanir raheem. Thanks to Allah for everything.
Coder: Abdullah Al Imran
Email: abdalimran@gmail.com */
#include<bits/stdc++.h>
using namespace std;
//2. Using Extended Euclidean Algorithm