CF992B Nastya Studies Informatics 数学（因子） 暴力求解 第三道

Nastya Studies Informatics

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Today on Informatics class Nastya learned about GCD and LCM (see links below). Nastya is very intelligent, so she solved all the tasks momentarily and now suggests you to solve one of them as well.

We define a pair of integers (a, b) good, if GCD(a, b) = x and LCM(a, b) = y, where GCD(a, b) denotes the greatest common divisor of a and b, and LCM(a, b) denotes the least common multiple of a and b.

You are given two integers x and y. You are to find the number of good pairs of integers (a, b) such that l ≤ a, b ≤ r. Note that pairs (a, b) and (b, a) are considered different if a ≠ b.

Input

The only line contains four integers l, r, x, y (1 ≤ l ≤ r ≤ 109, 1 ≤ x ≤ y ≤ 109).

Output

In the only line print the only integer — the answer for the problem.

Examples

input

Copy

1 2 1 2

output

Copy

2

input

Copy

1 12 1 12

output

Copy

4

input

Copy

50 100 3 30

output

Copy

0

Note

In the first example there are two suitable good pairs of integers (a, b): (1, 2) and (2, 1).

In the second example there are four suitable good pairs of integers (a, b): (1, 12), (12, 1), (3, 4) and (4, 3).

In the third example there are good pairs of integers, for example, (3, 30), but none of them fits the condition l ≤ a, b ≤ r.

给你四个数l，r，a，b，问在l到r的范围内有多少对数（两个数不能相同，顺序可以不同）满足gcd(x,y)=a,lcm(x,y)=b

枚举b的因子个数，再看这些因子每每两个的最大公约数是否等于a，等于a满足条件情况加一

#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 1e3 + 10;
typedef long long ll;
ll gcd( ll p, ll q ) {
    if( p == 0 ) {
        return q;
    }
    if( q == 0 ) {
        return p;
    }
    return gcd( q, p%q );
}
int main(){
    std::ios::sync_with_stdio(false);
    ll l, r, a, b;
    //cout << gcd( 16, 4 ) << endl;
    while( cin >> l >> r >> a >> b ) {
        ll num = 0;
        vector<ll> e;
        for( ll i = 1; i * i <= b; i ++ ) {
            if( b % i == 0 ) {
                e.push_back(i);
                if( i != b/i ) {
                    e.push_back(b/i);
                }
                //debug(i),debug(b/i);
            }
        }
        for( ll i = 0; i < e.size(); i ++ ) {
            for( ll j = 0; j < e.size(); j ++ ) {
                if( gcd( e[i], e[j] ) == a && e[i] * e[j] == a * b
                   && e[i] >= l && e[i] <= r && e[j] >= l && e[j] <= r ) {
                    num ++;
                }
            }
        }
        cout << num << endl;
    }
    return 0;
}