Problem: 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 a and screen height not greater than b. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is w, and the height of the screen is h, then the following condition should be met: w/h = x/y.

There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers w and h there is a TV set with screen width w and height h 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 w and h, beforehand, such that (w ≤ a), (h ≤ b) and (w/h = x/y).

In other words, Monocarp wants to determine the number of TV sets having aspect ratio x/y, screen width not exceeding a, and screen height not exceeding b. Two TV sets are considered different if they have different screen width or different screen height.

Input

The first line contains four integers a, b, x, y (1 ≤ a, b, x, y ≤ 10^{18}) — 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

17 15 5 3


Output

3


Input

14 16 7 22


Output

0


Input

4 2 6 4


Output

1


Input

1000000000000000000 1000000000000000000 999999866000004473 999999822000007597


Output

1000000063

Note

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

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.io.DataInputStream;
import java.io.FileInputStream;


public class Solution {

    static final long MD = 1000000007;
    public static void main(String[] args)throws IOException {


        long time = System.currentTimeMillis();
        Reader in = new Reader();
        long a = in.nextLong();
        long b = in.nextLong();
        long x = in.nextLong();
        long y = in.nextLong();

        long g = gcd(x, y);
        x = x/g;
        y = y/g;

        System.out.println(Math.min(a/x, b/y));
        in.close();
        
    } 
    static long gcd(long a, long b){
        if(a == 0)
            return b;
        return gcd(b%a, a);
    }
    static void printArr(int arr[], int s, int e){
        for(int i = s; i <= e; i++){
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }
    static void printArr(boolean arr[], int s, int e){
        for(int i = s; i <= e; i++){
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        private StringTokenizer st;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String line() throws IOException {
            byte[] buf = new byte[1000000]; // line length
            int cnt = 0, c = read();
            while (c <= ' ')
                c = read();
            do{
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }while ((c = read()) != -1);
            String s = new String(buf, 0, cnt);
            return s.trim();
        }
        public String str() throws IOException {
            byte[] buf = new byte[1000000]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == ' ')
                    break;
                buf[cnt++] = (byte) c;
            }
            String s = new String(buf, 0, cnt);
            return s;
        }
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();

            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';

            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }
        public int[] nextArr(int n) throws IOException {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++)
                arr[i] = this.nextInt();

            return arr;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}