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.*;
				        		    import java.math.*;
				        		    import java.util.*;
			import java.util.regex.Pattern;
			
				    	     
				        		    public class Main{
				        		  	private static InputStream stream;
				        		    	private static byte[] buf = new byte[1024];
				        		    	private static int curChar;
				        		    	private static int numChars;
				        		    	private static SpaceCharFilter filter;
				        		    	private static PrintWriter pw;
				        		    	private static long count = 0,mod=(long)1e9+7;
				        		    //	private static TreeSet<Integer> ts=new TreeSet[200000];
				public final static int INF = (int) 1E9;
				
				public static void main(String args[]) {
			    	
					InputReader(System.in);
					pw = new PrintWriter(System.out); 
				    new Thread(null ,new Runnable(){
				       public void run(){
				           try{
				        		
				               test();
			
				               pw.close();
				           } catch(Exception e){
				               e.printStackTrace();
				           }
				       }
				   },"1",1<<26).start();
				   	   }
				    static StringBuilder sb;
				    public static void test() throws IOException{
				    	 sb=new StringBuilder();
				    	
				    	 int t=1;
				    	 
				    	 while(t-->0){
				    		
				    		solve();
				    		//pw.println();
				    		//sb.append("\n");
				    	}
				    	//pw.println(sb);
				    }
				    
				    public static long pow(long n, long p,long mod) {
						if(p==0)
							return 1;
						if(p==1)
							return n%mod;
						if(p%2==0){
							long temp=pow(n, p/2,mod);
						return (temp*temp)%mod;
						}else{
							 	long temp=pow(n,p/2,mod);
							 	temp=(temp*temp)%mod;
							 	return(temp*n)%mod;
							 	
						}
					}
				    public static long pow(long n, long p) {
						if(p==0)
							return 1;
						if(p==1)
							return n;
						if(p%2==0){
							long temp=pow(n, p/2);
						return (temp*temp);
						}else{
							 	long temp=pow(n,p/2);
							 	temp=(temp*temp);
							 	return(temp*n);
							 	
						}
					}
				    public static void Merge(long a[],int p,int r){
				        if(p<r){
				            int q = (p+r)/2;
				            Merge(a,p,q);
				            Merge(a,q+1,r);
				            Merge_Array(a,p,q,r);
				        }
				    }
				    public static void Merge_Array(long a[],int p,int q,int r){
				       long b[] = new long[q-p+1];
				        long c[] = new long[r-q];
				        for(int i=0;i<b.length;i++)
				            b[i] = a[p+i];
				        for(int i=0;i<c.length;i++)
				            c[i] = a[q+i+1];
				        int i = 0,j = 0;
				        for(int k=p;k<=r;k++){
				            if(i==b.length){
				                a[k] = c[j];
				                j++;
				            }
				            else if(j==c.length){
				                a[k] = b[i];
				                i++;
				            }
				            else if(b[i]<c[j]){
				                a[k] = b[i];
				                i++;
				            }
				            else{
				                a[k] = c[j];
				                j++;
				            }
				        }
				    }
				    
				  
					public static long gcd(long x, long y) {
						if (x == 0)
							return y;
						else
							return gcd( y % x,x);
					}	
					
					public static boolean isPrime(int n) {
						if (n <= 1)
							return false;
						if (n <= 3)
							return true;
				 
						if (n % 2 == 0 || n % 3 == 0)
							return false;
				 
						for (int i = 5; i * i <= n; i = i + 6)
							if (n % i == 0 || n % (i + 2) == 0)
								return false;
				 
						return true;
					}
					
				        static LinkedList<Integer> adj[],adj2[];
				        static boolean Visited[];
				        static HashSet<Integer> exc;
				        static long oddsum[]=new long[1000001];
				        static long co=0;
				        static int indeg[],outdeg[];
		  		      
				    
				    	private static void buildgraph(int n){
				    		adj=new LinkedList[n+1];
				    		adj2=new LinkedList[n+1];
				    		Visited=new boolean[n+1];
				    		levl=new int[n+1];
				    		indeg=new int[n+1];
				    		outdeg=new int[n+1];
				    		for(int i=0;i<=n;i++){
				    			adj[i]=new LinkedList<Integer>();
				    			adj2[i]=new LinkedList<Integer>();
				    		}
				
				
				    	}
				      
				       
				        static int[] levl;
				        static int[] eat;
				        static int n,m;
				        static int price[];
				        //ind frog crab
				    
				        
				        static long d,x,y;
						static long modInverse(long A, long M)
						{
						extendedEuclid(A,M);
						return (x%M+M)%M;    //x may be negative
						}
						static void extendedEuclid(long A, long B) {
						if(B == 0) {
						d = A;
						x = 1;
						y = 0;
						}
						else {
						extendedEuclid(B, A%B);
						long temp = x;
						x = y;
						y = temp - (A/B)*y;
						}
						}
				        static double distance(int x1,int y1,int x2,int y2){
				        	return Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
				        }
				        static double area(int x1, int y1, int x2, int y2, int x3, int y3)
				        {
				           return Math.abs((x1*(y2-y3) + x2*(y3-y1)+ x3*(y1-y2))/2.0);
				        }
				        static boolean isInside(int x1, int y1, int x2, int y2, int x3, int y3, int x, int y)
				        {   
				           double A = area (x1, y1, x2, y2, x3, y3);
				         
				           double A1 = area (x, y, x2, y2, x3, y3);
				         
				           double A2 = area (x1, y1, x, y, x3, y3);
				         
				           double A3 = area (x1, y1, x2, y2, x, y);
				           
				          return (A == A1 + A2 + A3);
				        }
				      
						static int col[];
				    public static boolean isVowel(char c){
				    	if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
				    		return true;
				    	return false;
				    }
				static long arr[], lazy[],ans[];
				static int c[],nodes[];
				static int dp[][];
				static long a[][];
				
				private static boolean isPrim(long n,int p){
					for (long i = 2; i * i <= n; i++) {
				        if (n % i == 0 && i <= p) return false;
				    }
				    return true;
				}
				//price - starting index of string with given hash
				//rating-count of number of time of a hash
				static ArrayList<String> all_perm;
				static boolean[][] visited1;
				static  boolean won;
				static boolean containsCycle;
				static ArrayList<Integer> anss;
				static int index = 0;
				static int trav[],subtree[];
			public static void solve() throws IOException{
				long a  =nextLong();
				long b = nextLong();
				long x = nextLong();
				long y = nextLong();
				
				long gcd = gcd(x,y);
				x/=gcd;
				y/=gcd;
				long max_poss_x = a/x;
				long max_poss_y = b/y;
				pw.println(Math.min(max_poss_y, max_poss_x));
			}
		
			
			static int res=0;
			private static void dfs(int start, int par){
				Visited[start] = true;
				trav[index] = start;
				index++;
				for(int x: adj[start]){
					if(!Visited[x]){
						dfs(x, start);
					}
				}
				subtree[start]++;
				subtree[par]+=subtree[start];
			}
			
						private static boolean check(int x,int y,int n,int m){
					if(x>=0 && x<n && y>=0 && y<m)
						return true;
					return false;
				}
						
						
						
									
				
				    private static boolean Check(int x,int y,int n){
						if(x>=0 && x<n && y>=0 && y<n)
							return true;
						return false;
					}
				    
				    public static String reverseString(String s) {
						StringBuilder sb = new StringBuilder(s);
						sb.reverse();
						return (sb.toString());
					}
				    
				  /*  
				   private static void BFS(int sou){
				    	Queue<Integer> q=new LinkedList<Integer>();
				    	q.add(sou);
				    	Visited[sou]=true;
				    	levl[sou]=0;
				    	while(!q.isEmpty()){
				    		int top=q.poll();
				    		
				    		for(int i:adj[top]){
				    			//pw.println(i+" "+top);
							if(!Visited[i])
							{
								
								q.add(i);
								levl[i]=levl[top]+1;
							}
							
							Visited[i]=true;
							
							}
						}
					}*/
					
				
				
				
				    		      
				    		   /* private static void kahn(int n){
				    		    	
				    		    	PriorityQueue<Integer> q=new PriorityQueue<Integer>();
				    				for(int i=1;i<=n;i++){
				    					if(indeg[i]==0){
				    						q.add(i);
				    					}
				    				}
				    				while(!q.isEmpty()){
				    					int top=q.poll();
				    					st.push(top);
				    					for(Node i:adj[top]){
				    						indeg[i.to]--;
				    						if(indeg[i.to]==0){
				    							q.add(i.to);
				    						}
				    					}
				    				}
				    		    }
				    		        
				    		        static int state=1;
				    		        static long no_exc=0,no_vert=0;
				    		      static Stack<Integer> st;
				    		      static HashSet<Integer> inset;
				    		     /*   private static void topo(int curr){
				    		        	
				    		        	Visited[curr]=true;
				    		        	inset.add(curr);
				    		        	for(int x:adj[curr]){
				    		        		if(adj[x].contains(curr) || inset.contains(x)){
				    		        			state=0;
				    		        			return;
				    		        		}
				    		        		if(state==0)
				    		        			return;
				    		        		
				    		        	}
				    		        	st.push(curr);
				    		        	
				    		        	inset.remove(curr);
				    		        }*/
				    		        static HashSet<Integer> hs;
				    		       
				    		     
				    		     	static boolean prime[];
									static int spf[];
									public static void sieve(int n){
										prime=new boolean[n+1];
										spf=new int[n+1];
										
										Arrays.fill(spf, 1);
										Arrays.fill(prime, true);
									prime[1]=false;
										spf[2]=2;
										
									for(int i=4;i<=n;i+=2){
										spf[i]=2;
									}
									for(int i=3;i<=n;i+=2){
										if(prime[i]){
											spf[i]=i;
											for(int j=2*i;j<=n;j+=i){
												
												prime[j]=false;
											if(spf[j]==1){
												spf[j]=i;
											}
											}
										}
									}
									
										
									}
				    		     	
				    		    	// To Get Input
				// Some Buffer Methods
				 
				    		     	public static void sort(long a[]){
				    		     		Merge(a, 0, a.length-1);
				    		     	}
				    		    	public static void InputReader(InputStream stream1) {
				    		    		stream = stream1;
				    		    	}
				 
				    		    	private static boolean isWhitespace(int c) {
				    		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				    		    	}
				 
				    		    	private static boolean isEndOfLine(int c) {
				    		    		return c == '\n' || c == '\r' || c == -1;
				    		    	}
				 
				    		    	private static int read() {
				    		    		if (numChars == -1)
				    		    			throw new InputMismatchException();
				    		    		if (curChar >= numChars) {
				    		    			curChar = 0;
				    		    			try {
				    		    				numChars = stream.read(buf);
				    		    			} catch (IOException e) {
				    		    				throw new InputMismatchException();
				    		    			}
				    		    			if (numChars <= 0)
				    		    				return -1;
				    		    		}
				    		    		return buf[curChar++];
				    		    	}
				 
				    		    	private static int nextInt() {
				    		    		int c = read();
				    		    		while (isSpaceChar(c))
				    		    			c = read();
				    		    		int sgn = 1;
				    		    		if (c == '-') {
						sgn = -1;
						c = read();
					}
					int res = 0;
					do {
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
				    		    			c = read();
				    		    		} while (!isSpaceChar(c));
				    		    		return res * sgn;
				    		    	}
				 
				    		    	private static long nextLong() {
				    		    		int c = read();
				    		    		while (isSpaceChar(c))
				    		    			c = read();
				    		    		int sgn = 1;
				    		    		if (c == '-') {
						sgn = -1;
						c = read();
					}
					long res = 0;
					do {
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
				    		    			c = read();
				    		    		} while (!isSpaceChar(c));
				    		    		return res * sgn;
				    		    	}
				 
				    		    	private static String nextToken() {
				    		    		int c = read();
				    		    		while (isSpaceChar(c))
				    		    			c = read();
				    		    		StringBuilder res = new StringBuilder();
				    		    		do {
				    		    			res.appendCodePoint(c);
				    		    			c = read();
				    		    		} while (!isSpaceChar(c));
				    		    		return res.toString();
				    		    	}
				 
				    		    	private static String nextLine() {
				    		    		int c = read();
				    		    		while (isSpaceChar(c))
				    		    			c = read();
				    		    		StringBuilder res = new StringBuilder();
				    		    		do {
				    		    			res.appendCodePoint(c);
				    		    			c = read();
				    		    		} while (!isEndOfLine(c));
				    		    		return res.toString();
				    		    	}
				 
				    		    	private static int[] nextIntArray(int n) {
				    		    		int[] arr = new int[n];
				    		    		for (int i = 0; i < n; i++) {
				    		    			arr[i] = nextInt();
				    		    		}
				    		    		return arr;
				    		    	}
				 
				    		    	private static long[][] next2dArray(int n, int m) {
				    		    		long[][] arr = new long[n][m];
				    		    		for (int i = 0; i < n; i++) {
				    		    			for (int j = 0; j < m; j++) {
				    		    				arr[i][j] = nextLong();
				    		    			}
				    		    		}
				    		    		return arr;
				    		    	}
				    		    	private static char[][] nextCharArray(int n,int m){
				    		    		char [][]c=new char[n][m];
				    		    		for(int i=0;i<n;i++){
				    		    			String s=nextLine();
				    		    			for(int j=0;j<s.length();j++){
				    		    				c[i][j]=s.charAt(j);
				    		    			}
				    		    		}
				    		    		return c;
				    		    	}
				 
				    		    	private static long[] nextLongArray(int n) {
				    		    		long[] arr = new long[n];
				    		    		for (int i = 0; i < n; i++) {
				    		    			arr[i] = nextLong();
				    		    		}
				    		    		return arr;
				    		    	}
				 
				    		    	private static void pArray(int[] arr) {
				    		    		for (int i = 0; i < arr.length; i++) {
				    		    			pw.print(arr[i] + " ");
				    		    		}
				    		    		pw.println();
				    		    		return;
				    		    	}
				 
				    		    	private static void pArray(long[] arr) {
				    		    		for (int i = 0; i < arr.length; i++) {
				    		    			pw.print(arr[i] + " ");
				    		    		}
				    		    		pw.println();
				    		    		return;
				    		    	}
				 
				    		    	private static void pArray(boolean[] arr) {
				    		    		for (int i = 0; i < arr.length; i++) {
				    		    			pw.print(arr[i] + " ");
				    		    		}
				    		    		pw.println();
				    		    		return;
				    		    	}
				 
				    		    	private static boolean isSpaceChar(int c) {
				    		    		if (filter != null)
				    		    			return filter.isSpaceChar(c);
				    		    		return isWhitespace(c);
				    		    	}
				 
				    		    	private interface SpaceCharFilter {
				    		    		public boolean isSpaceChar(int ch);
				    		    	}
				    		    	
				
				}
				    		    
				    		        class Node{
				    		    	int to;
				    		    	long dist;
				    		    	Node(int to,long dist){
				    		    		this.to=to;
				    		    		this.dist=dist;
				    		    	}
				    		    	
				    		    }
				    		        class Qu{
				    		    		long a0,a1,a2,a3;
				    		    		public Qu(long a0,long a1,long a2,long a3) {
				    		    			this.a0=a0;
				    		    			this.a1=a1;
				    		    			this.a2=a2;
				    		    			this.a3=a3;
				    		    		}
				    		    }
				    		
				class Dsu{
				private int rank[], parent[] ,n;
				long str[],si[],larg[];
				long max=0;
				int cnt=0;
				private static int[] parent1;
				Dsu(int size){
					this.n=size+1;
					rank=new int[n];
					cnt=n-1;
					//parent=new int[n];
				    		    		    		parent=new int[n];
				    		    		    		str=new long[n];
				    		    		    		si=new long[n];
				    		    		
				    		    		    		larg=new long[n];
				    		    		    		makeSet();
				    		    		
				    		    		    	}
				    		    		    	
				    		    		    	void makeSet(){
				    		    		    		for(int i=0;i<n;i++){
				    		    		    			parent[i]=i;
				    		    		    			si[i]=1;
				    		    		    		}
				    		    		    	}
				    		    		    	
				    		    		    	int find(int x){
				    		    		    		if(parent[x]!=x){
				    		    		    			
				    		    		    			parent[x]=find(parent[x]);
				    		    		    		}
				    		    		    		return parent[x];
				    		    		    	}
				    		    		    	
				    		    		    	void join(int ind,long val){
				    		    		    		if(str[ind]==0){
				    		    		    			str[ind]=val;
				    		    		    			larg[ind]=val;
				    		    		    			max=Math.max(max, str[ind]);
				    		    		    		}
				    		    		    		int prev_ind=(ind-1);
				    		    		    		int next_ind=(ind+1);
				    		    		    		if(prev_ind>0 && larg[prev_ind]!=0){
				    		    		    			union(prev_ind,ind);
				    		    		    		}
				    		    		    		if(next_ind<n && larg[next_ind]!=0){
				    		    		    			union(next_ind,ind);
				    		    		    		}
				    		    		    		
				    		    		    	}
				    		    		    
				    		    		    	
				    		    		    	boolean union(int x,int y){
				    		    		    		int xRoot=find(x);
				    		    		    		int yRoot=find(y);
				    		    		    
				    		    		    	
				    		    		    		if(xRoot==yRoot)
				    		    		    			return false;
				    		    		    		if(rank[xRoot]<rank[yRoot]){
				    		    		    		parent[xRoot]=yRoot;
				    		    		    		
				    		    		    		larg[yRoot]=Math.max(larg[xRoot], larg[yRoot]);
				    		    		    		
				    		    		    		si[yRoot]+=si[xRoot];
				    		    		    		str[yRoot]=larg[yRoot]*si[yRoot];
				    		    		    			max=Math.max(str[yRoot], max);
				    		    		    		}else if(rank[yRoot]<rank[xRoot]){
				    		    		    			parent[yRoot]=xRoot;
				     
				    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
				        		    		    		
				        		    		    		si[xRoot]+=si[yRoot];
				        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
				    			    		    		max=Math.max(str[xRoot], max);
				    		    		    		}else{
				    		    		    			parent[yRoot]=xRoot;
				    		    		    			rank[xRoot]++;
				     
				    		    		    			larg[xRoot]=Math.max(larg[xRoot], larg[yRoot]);
				        		    		    		
				        		    		    		si[xRoot]+=si[yRoot];
				        		    		    		str[xRoot]=larg[xRoot]*si[xRoot];
				    			    		    		max=Math.max(str[xRoot], max);
				    		    		    		
				    		    		    		}
				    		    		    		cnt--;
				    		    		    		return true;
				    		    		    	}
				    	
				    		    		     
				    		    		    }
			class Pair1 implements Comparable<Pair1>{
					long l,b;
					Pair1(long l,long b){
						this.l=l;
						this.b=b;
					}
					@Override
					public int compareTo(Pair1 arg0) {
						if(arg0.l == l){
							long area1 = arg0.l * arg0.b;
							long area2 = l * b;
							return (int)(area1 - area2);
						}
						return (int)(l - arg0.l);
							
						
					}
				
				
				}