Problem:
Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <time.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef vector<ll> vec;
typedef vector<vec> vec2;
typedef map<ll,ll> MPll;
typedef set<ll> setl;

const ll INF = 1ll << 60;
const ld EPS = 1e-10;
const int dx[4] = {1,0,-1,0};
const int dy[4] = {0,1,0,-1};
const ll MOD = 1000000007;

//for文
#define FOR(i,a,b) for(ll i = (ll)a;i < (ll)b;i++)
#define FORE(i,a,b) for(ll i = (ll) a;i <= (ll) b;i++ )
#define REP(i,size)  for(ll i =(ll)0;i<size;i++)
#define REPE(i,size)  for(ll i =(ll)0;i<=size;i++)
#define REPR(i,size)  for(ll i =(ll)size;i>=0;i--)
#define FOREACH(it, vec) for (auto it = vec.begin(); it != vec.end(); it++)

//ソート
#define ALL(vec) (vec).begin(),(vec).end()
#define SORT(vec) sort(ALL(vec))
#define SORTA(arr) sort(arr,arr + (sizeof(arr) / sizeof(ll)))
#define INVSORT(vec) sort((vec).rbegin(),(vec).rend())
#define REV(vec) reverse(ALL(vec))
#define REVA(arr) reverse(arr,arr + (sizeof(arr) / sizeof(ll)))
#define INVSORTA(arr) sort(arr,arr + (sizeof(arr) / sizeof(ll))),REVA(arr)

//最大値最小値
#define MAX(vec) *max_element(ALL(vec))
#define UNIQ(vec) SORT(vec);vec.erase(unique(ALL(vec)),vec.end())
#define MIN(vec) *min_element(ALL(vec))

//出力
#define printl(a) cout << a << "\n"
#define print(a) cout << a
#define OUT(a) printf("%lld\n",a)
#define OUTA(array) REP(i,sizeof(array)/sizeof(ll)) printf("%lld\n",array[i])
#define OUTV(vec) REP(i,vec.size()) printf("%lld\n",vec[i])
#define SP printf(" ")

//入力
#define IN(x) scanf("%lld",&x)
#define INV(vec) REP(i,vec.size()) scanf("%lld",&vec[i])
#define INA(array) REP(i,sizeof(array)/sizeof(ll)) scanf("%lld",array + i)
#define INS(x) cin >> x
#define INCH(x) scanf(" %c",&x)

//型
#define P pair
#define vp vector<P>
#define F first
#define S second

//その他
#define PB push_back
#define MP make_pair
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,-1,sizeof(a))
#define INFI(a) memset(a,INF,sizeof(a))
#define MEM(a,b) memset(a,(b),sizeof(a))
#define MEMSET(v, h) memset((v), h, sizeof(v))


//関数
template<class T> inline void amax(T &a,const T &b) { if(a < b) a = b; }
template<class T> inline void amin(T &a, const T &b) { if(a > b) a = b; }


/*
struct structure{
    ll num1,num2,string s;
    bool operator<(const rest &another) const{
        return this->s < another.s;
    }
    structure(ll a,ll b,string s){
        this->num1 = a,this->num2=b,this->s=s;
    }
};a
*/
//特殊
//#define int ll
#define _CRT_SECURE_NO_WARNINGS



/*
template <typename T>
struct UnionFindTree{

    vector<T> par;

    UnionFindTree(T n) : par(n+1){
        for (int i = 1; i <= n; ++i) {
            par[i] = i;
        }
    }

    T root(T x){
        if(par[x] == x) return x;
        else  return par[x] = root(par[x]);
    }

    void unite(T x,T y){
        if(!same(x,y)) par[root(x)] = root(par[y]);
    }

    T same(T x,T y){
        return root(x) == root(y);
    }

};
*/

struct edge { 
    int to, length;

    edge(ll to,ll length){
        this->to = to,this->length=length;
    }
};



vec dijkstra(const vector<vector<edge>> &graph, ll start) {
    vec min_dis(graph.size(), INF);
    set<pair<ll,ll>> miru;
    min_dis[start] = 0;

    miru.insert({0,start});

    while (!miru.empty()) {
        ll cur = miru.begin()->second;
        miru.erase(miru.begin());
        for (auto it: graph[cur]) {
            ll temp = min_dis[cur] + it.length;
            if (min_dis[it.to] > temp) {
                miru.erase({min_dis[it.to], it.to});
                min_dis[it.to] = temp;
                miru.insert({min_dis[it.to], it.to});
            }
        }
    }

    return min_dis;


}

//#define DEBUG

#ifdef DEBUG
#define debugl(x) cerr << #x << ":" << x<<"\n"
    #define debug(x)  cerr << x<<endl;
    #define  debugV(V) REP(i,V.size()){cerr << i << ":" << V[i]<<endl;}
    #define  debugA(A) REP(i,sizeof(A)/sizeof(ll)){cerr << i << ":" << V[i]<<endl;}
#else
#define debug(x)
#define debugV(x)
#define debugA(x)
#endif

#define ZERO(a) memset(a,0,sizeof(a))
#define ALL(vec) (vec).begin(),(vec).end()
#define SORT(vec) sort(ALL(vec))

std::vector<bool> IsPrime;

void sieve(size_t max){
    if(max+1 > IsPrime.size()){     // resizeで要素数が減らないように
        IsPrime.resize(max+1,true); // IsPrimeに必要な要素数を確保
    }
    IsPrime[0] = false; // 0は素数ではない
    IsPrime[1] = false; // 1は素数ではない

    for(size_t i=2; i*i<=max; ++i) // 0からsqrt(max)まで調べる
        if(IsPrime[i]) // iが素数ならば
            for(size_t j=2; i*j<=max; ++j) // (max以下の)iの倍数は
                IsPrime[i*j] = false;      // 素数ではない
}

ll N,W;

int gcd(int a, int b)
{
    if (a == 0)
        return b;
    return gcd(b%a, a);
}


int commDiv(int a,int b)
{
    int n = gcd(a, b);

    int result = 0;
    for (int i=1; i<=sqrt(n); i++)
    {
        if (n%i==0)
        {
            if (n/i == i)
                result += 1;
            else
                result += 2;
        }
    }
    return result;
}


int main(){
    set<ll> divisor;
    ll a,b;
    IN(a);IN(b);
    float temp;
    ll tempin;
    if (a >= b){
         tempin = b;
    }else{
        tempin = a;
    }
    temp = sqrt(tempin);

    FOR(i,1,temp+1){
        if(a % i == 0 and b % i == 0){
         divisor.insert(i) ;
        }
    }

    sieve(tempin);

    ll ans = 0;

    for(auto it:divisor){
        if(IsPrime[it]) ans++;
    }

    OUT(ans+1);


}