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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.BufferedWriter;
import java.io.IOException;
import java.util.HashMap;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        CNekoDoesMaths solver = new CNekoDoesMaths();
        solver.solve(1, in, out);
        out.close();
    }

    static class CNekoDoesMaths {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            // out.setBoolLabel(LightWriter.BoolLabel.YES_NO_FIRST_UP);
            long a = in.longs(), b = in.longs();
            if (a > b) {
                long t = a;
                a = b;
                b = t;
            }

            if (a == 1 || a % b == 0) {
                out.ans(0).ln();
                return;
            }

            long d = b - a;
            long maxk = (a + d - 1) / d * d - a;
            long gcd = IntMath.gcd(a + maxk, b + maxk);

            long ansk = 0, ansv = IntMath.lcm(a, b);
            List<Map.Entry<Long, Integer>> es = new ArrayList<>(IntMath.primeFactorize(gcd).entrySet());
            long itr = 1;
            for (Map.Entry<Long, Integer> ent : es) {
                itr *= ent.getValue() + 1;
            }
            for (int i = 0; i < itr; i++) {
                long g = 1;
                int t = i;
                for (Map.Entry<Long, Integer> ent : es) {
                    int p = t % (ent.getValue() + 1);
                    t /= (ent.getValue() + 1);
                    while (p > 0) {
                        g *= ent.getKey();
                        p--;
                    }
                }

                long k = (a + g - 1) / g * g - a;
                long lcm = IntMath.lcm(a + k, b + k);
                if (lcm < ansv) {
                    ansv = lcm;
                    ansk = k;
                }
            }

            out.ans(ansk).ln();
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new BufferedWriter(new OutputStreamWriter(out, Charset.defaultCharset())));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static final class IntMath {
        private IntMath() {
        }

        public static long lcm(long a, long b) {
            return a / gcd(a, b) * b;
        }

        public static long gcd(long a, long b) {
            long t;
            while (a % b > 0) {
                t = b;
                b = a % b;
                a = t;
            }
            return b;
        }

        public static Map<Long, Integer> primeFactorize(long p) {
            Map<Long, Integer> factor = new HashMap<>();
            if ((p & 1) == 0) {
                int c = 0;
                do {
                    c++;
                    p >>= 1;
                } while ((p & 1) == 0);
                factor.put(2L, c);
            }
            for (long i = 3; i * i <= p; i += 2) {
                if (p % i == 0) {
                    int c = 0;
                    do {
                        c++;
                        p /= i;
                    } while ((p % i) == 0);
                    factor.put(i, c);
                }
            }
            if (p > 1) {
                factor.put(p, 1);
            }
            return factor;
        }

    }

    static class LightScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long longs() {
            return Long.parseLong(string());
        }

    }

    static interface Verified {
    }
}

