Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.

Neko has two integers a and b. His goal is to find a non-negative integer k such that the least common multiple of a+k and b+k is the smallest possible. If there are multiple optimal integers k, he needs to choose the smallest one.

Given his mathematical talent, Neko had no trouble getting Wrong Answer on this problem. Can you help him solve it?

Input

The only line contains two integers a and b (1 ≤ a, b ≤ 10^9).

Output

Print the smallest non-negative integer k (k ≥ 0) such that the lowest common multiple of a+k and b+k is the smallest possible.

If there are many possible integers k giving the same value of the least common multiple, print the smallest one.

Examples

Input


6 10


Output


2

Input


21 31


Output


9

Input


5 10


Output


0

Note

In the first test, one should choose k = 2, as the least common multiple of 6 + 2 and 10 + 2 is 24, which is the smallest least common multiple possible.
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer; 
				  
				
				public class temp4 {
					static class FastReader 
				    { 
				        BufferedReader br; 
				        StringTokenizer st; 
				  
				        public FastReader() 
				        { 
				            br = new BufferedReader(new
				                     InputStreamReader(System.in)); 
				        } 
				  
				        String next() 
				        { 
				            while (st == null || !st.hasMoreElements()) 
				            { 
				                try
				                { 
				                    st = new StringTokenizer(br.readLine()); 
				                } 
				                catch (IOException  e) 
				                { 
				                    e.printStackTrace(); 
				                } 
				            } 
				            return st.nextToken(); 
				        } 
				  
				        int nextInt() 
				        { 
				            return Integer.parseInt(next()); 
				        } 
				  
				        long nextLong() 
				        { 
				            return Long.parseLong(next()); 
				        } 
				  
				        double nextDouble() 
				        { 
				            return Double.parseDouble(next()); 
				        } 
				  
				        String nextLine() 
				        { 
				            String str = ""; 
				            try
				            { 
				                str = br.readLine(); 
				            } 
				            catch (IOException e) 
				            { 
				                e.printStackTrace(); 
				            } 
				            return str; 
				        } 
				    } 
					
				/*	static class Reader 
				    { 
				        final private int BUFFER_SIZE = 1 << 16; 
				        private DataInputStream din; 
				        private byte[] buffer; 
				        private int bufferPointer, bytesRead; 
				  
				        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 readLine() throws IOException 
				        { 
				            byte[] buf = new byte[64]; // line length 
				            int cnt = 0, c; 
				            while ((c = read()) != -1) 
				            { 
				                if (c == '\n') 
				                    break; 
				                buf[cnt++] = (byte) c; 
				            } 
				            return new String(buf, 0, cnt); 
				        } 
				  
				        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; 
				        } 
				  
				        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(); 
				        } 
				    } */
					static class Print
				{
					    private final BufferedWriter bw;
					    public Print()
					    {
					        bw=new BufferedWriter(new OutputStreamWriter(System.out));
					    }
				    public void print(String str)throws IOException
					    {
					        bw.append(str);
					    }
					    public void println(String str)throws IOException
					    {
					        print(str);
					        bw.append("\n");
					    }
					    public void close()throws IOException
					    {
					        bw.close();
					    }} 
						
						
						static long a=0,b=0,diff=0,ans=0,min=Long.MAX_VALUE;
						public static void main(String[] args) throws IOException {			
							FastReader scn=new FastReader();
							Print pr=new Print();
							a=scn.nextLong();b=scn.nextLong();
							if(a==b){
								pr.println("0");
							}else{
							diff=Math.abs(a-b);
							for(long i=1;i*i<=diff;i++){
								if(diff%i==0){
								update(i);update(diff/i);
								}
							}
							pr.println(ans+"");
							}
							pr.close();
							
						}
						public static void update(long x){
							long t=(x-a%x)%x;
							long tmin=(a+t)/x*(b+t);
							if(min==tmin)ans=Math.min(ans, t);
							if(tmin<min){
								min=tmin;
								ans=t;
							}
						}
					
					
							public static class node{
							int a;
							int b;
							public node(int a,int b){
								this.a=a;this.b=b;
							}
						}
						
				}
					