B. Buying a TV Set

滴答滴答---题目链接

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than aa and screen height not greater than bb. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is ww, and the height of the screen is hh, then the following condition should be met: wh=xywh=xy.

There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers ww and hh there is a TV set with screen width ww and height hh in the shop.

Monocarp isn't ready to choose the exact TV set he is going to buy. Firstly he wants to determine the optimal screen resolution. He has decided to try all possible variants of screen size. But he must count the number of pairs of positive integers ww and hh, beforehand, such that (w≤a)(w≤a), (h≤b)(h≤b) and (wh=xy)(wh=xy).

In other words, Monocarp wants to determine the number of TV sets having aspect ratio xyxy, screen width not exceeding aa, and screen height not exceeding bb. Two TV sets are considered different if they have different screen width or different screen height.

Input

The first line contains four integers aa, bb, xx, yy (1≤a,b,x,y≤10181≤a,b,x,y≤1018) — the constraints on the screen width and height, and on the aspect ratio.

Output

Print one integer — the number of different variants to choose TV screen width and screen height so that they meet the aforementioned constraints.

Examples

input

Copy

17 15 5 3

output

Copy

input

Copy

14 16 7 22

output

Copy

input

Copy

4 2 6 4

output

Copy

input

Copy

1000000000000000000 1000000000000000000 999999866000004473 999999822000007597

output

Copy

1000000063

Note

In the first example, there are 33 possible variants: (5,3)(5,3), (10,6)(10,6), (15,9)(15,9).

In the second example, there is no TV set meeting the constraints.

In the third example, there is only one variant: (3,2)(3,2).

题意：

有一个商店出售电视机，这个商店拥有每一种宽不超过a并且高不超过b的电视机。

现在Monocarp想买一台电视机，但是他要求这台电视级的宽高比等于一个给定的分数 $\frac{x}{y}$ ，求有多少种方案。

一句话题意：给你 $a,b,x,y$ ，求满足 $\frac{w}{h}=\frac{x}{y}$ 的 $(w,h)$ 对数，其中 $1\leq w\leq a$ ， $1\leq h\leq b$ 。

题解：

显然面对 $10^{18}$ 范围内的 $a,b$ ，不能枚举。

我们考虑，将 $\frac{x}{y}$ 化简为最简分数 $\frac{q}{p}$ ，则有 $\frac{w}{h}=\frac{q}{p}$ ，那么 $w=kq,h=kp$ ， $k$ 为正整数， $1\leq w\leq a$ ， $1\leq h\leq a$ 。

考虑到 $w$ 有 $\left \lfloor \frac{a}{q} \right \rfloor$ 种取值， $h$ 有 $\left \lfloor \frac{b}{p} \right \rfloor$ 种取值，那么答案为 $min(\left \lfloor \frac{a}{q} \right \rfloor,\left \lfloor \frac{b}{p} \right \rfloor)$ 。

时间复杂度： $O(log(min(x,y)))$ （求gcd所用时间）

代码：

#include <bits/stdc++.h>
using namespace std;
int main()
{
    long long int a,b,x,y,t;
    cin>>a>>b>>x>>y;
    t=__gcd(x,y);
    x=x/t;
    y=y/t;
    long long int ans;
        a=a/x;
        b=b/y;
        ans=min(a,b);
    cout<<ans<<endl;
    return 0;
}

题意：

题解：

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