Problem: Recently a Golden Circle of Beetlovers was found in Byteland. It is a circle route going through n ⋅ k cities. The cities are numerated from 1 to n ⋅ k, the distance between the neighboring cities is exactly 1 km.

Sergey does not like beetles, he loves burgers. Fortunately for him, there are n fast food restaurants on the circle, they are located in the 1-st, the (k + 1)-st, the (2k + 1)-st, and so on, the ((n-1)k + 1)-st cities, i.e. the distance between the neighboring cities with fast food restaurants is k km.

Sergey began his journey at some city s and traveled along the circle, making stops at cities each l km (l > 0), until he stopped in s once again. Sergey then forgot numbers s and l, but he remembers that the distance from the city s to the nearest fast food restaurant was a km, and the distance from the city he stopped at after traveling the first l km from s to the nearest fast food restaurant was b km. Sergey always traveled in the same direction along the circle, but when he calculated distances to the restaurants, he considered both directions.

Now Sergey is interested in two integers. The first integer x is the minimum number of stops (excluding the first) Sergey could have done before returning to s. The second integer y is the maximum number of stops (excluding the first) Sergey could have done before returning to s.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 100 000) — the number of fast food restaurants on the circle and the distance between the neighboring restaurants, respectively.

The second line contains two integers a and b (0 ≤ a, b ≤ k/2) — the distances to the nearest fast food restaurants from the initial city and from the city Sergey made the first stop at, respectively.

Output

Print the two integers x and y.

Examples

Input


2 3
1 1


Output


1 6


Input


3 2
0 0


Output


1 3


Input


1 10
5 3


Output


5 5

Note

In the first example the restaurants are located in the cities 1 and 4, the initial city s could be 2, 3, 5, or 6. The next city Sergey stopped at could also be at cities 2, 3, 5, 6. Let's loop through all possible combinations of these cities. If both s and the city of the first stop are at the city 2 (for example, l = 6), then Sergey is at s after the first stop already, so x = 1. In other pairs Sergey needs 1, 2, 3, or 6 stops to return to s, so y = 6.

In the second example Sergey was at cities with fast food restaurant both initially and after the first stop, so l is 2, 4, or 6. Thus x = 1, y = 3.

In the third example there is only one restaurant, so the possible locations of s and the first stop are: (6, 8) and (6, 4). For the first option l = 2, for the second l = 8. In both cases Sergey needs x=y=5 stops to go to s.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
 
 
public class Myclass {
    static ArrayList a[]=new ArrayList[3000001];
    static ArrayList child[]=new ArrayList[3000001];
	static boolean visited[]=new boolean [1000001];
	static int val[]=new int[300001];
	static boolean  chk[]=new boolean [300001];
	static int parent[]=new int[300001];
	static Vector<Integer>ans=new Vector<>();
	static void dfs(int n) {
		visited[n]=true;
		boolean pos=true;
		for(int i=0;i<a[n].size();i++) {
			int id=(int) a[n].get(i);
			if(!visited[id]) {
				parent[id]=n;
				dfs(id);
				child[n].add(id);
				pos&=(val[id]==1)?true:false;
			}
		}
		chk[n]=pos;
	}
	static void cal(int n) {
		for(int i=1;i<=n;i++) {
			if(chk[i] && val[i]==1) {
				ans.add(i);
				for(int j=0;j<child[i].size();j++) {
					int id=(int) child[i].get(j);
					chk[parent[i]]&=(val[id]==1)?true:false;
					parent[id]=parent[i];
				}
			}
		}
	}
     public static void main(String[]args)
    {
        InputReader in=new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        long n=in.nextLong();
        long k=in.nextLong();
        long  a=in.nextLong();
        long  b=in.nextInt();
        long mini=Long.MAX_VALUE;
        long maxi=Long.MIN_VALUE;
        for(long i=0;i<=n;i++) {
        	long  val=i*k+(a+b);
        	long val1=i*k+(k-a+b);
        	if(val<=n*k) {
        		long gcd=GCD(val,n*k);
        		mini=Math.min(mini, (n*k)/gcd);
        		maxi=Math.max(maxi, (n*k)/gcd);
        	}
        	if(val1<=n*k) {
        		long gcd=GCD(val1,n*k);
        		mini=Math.min(mini, (n*k)/gcd);
        		maxi=Math.max(maxi, (n*k)/gcd);

        	}
        }
        pw.println(mini+" "+maxi);
        pw.flush();
        pw.close();
 
    }
    private static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
   static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
   public static long modularExponentiation(long x,long n,long M)
   {
       long result=1;
       while(n>0)
       {
           if(n % 2 ==1)
               result=(result%M * x%M)%M;
           x=(x%M * x%M)%M;
           n=n/2;
       }
       return result;
   }
   
   public static long modInverse(int A,int M)
   {
       return modularExponentiation(A,M-2,M);
   }
   
   public static long modInverse(long A,long M)
   {
       return modularExponentiation(A,M-2,M);
   }
    static class pair implements Comparable<pair>{
        Integer x;
        Integer y;

        pair(int x,int w){
            this.x=x;
            this.y=w;
        }
        
        public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
            return result;
            }  
         public String toString(){
            return (x+" "+y);
        }
  }
    public static long GCD(long a,long b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }
  static class query{
      Long x;
      Long y;
      Integer z;
      query(long x,long y,int z){
          this.x=x;
          this.y=y;
          this.z=z;
      }
  }
    
}