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.util.*;

import javax.lang.model.util.ElementScanner6;

import java.io.*;

public class Main {

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();

    }





    static class Solver {

        class Node implements Comparable < Node > {
            int i;
            int cnt;

            Node(int i, int cnt) {
                this.i = i;
                this.cnt = cnt;
            }

            public int compareTo(Node n) {
                if (this.cnt == n.cnt) {
                    return Integer.compare(this.i, n.i);
                }
                return Integer.compare(this.cnt, n.cnt);
            }
        }

        public boolean done(int[] sp, int[] par) {
            int root;

            root = findSet(sp[0], par);

            for (int i = 1; i < sp.length; i++) {
                if (root != findSet(sp[i], par))
                    return false;
            }
            return true;
        }
        public int findSet(int i, int[] par) {
            int x = i;
            boolean flag = false;
            while (par[i] >= 0) {
                flag = true;
                i = par[i];
            }
            if (flag)
                par[x] = i;
            return i;
        }

        public void unionSet(int i, int j, int[] par) {
            int x = findSet(i, par);
            int y = findSet(j, par);
            if (x < y) {
                par[y] = x;
            } else {
                par[x] = y;
            }
        }

        public long pow(long a, long b, long MOD) {
            if (b == 0) {
                return 1;
            }
            if (b == 1) {
                return a;
            }
            long val = pow(a, b / 2, MOD);
            if (b % 2 == 0) {
                return val * val % MOD;
            } else {
                return val * (val * a % MOD) % MOD;

            }

        }


        public void minPrimeFactor(int n, int[] s) {
            boolean prime[] = new boolean[n + 1];
            Arrays.fill(prime, true);
            s[1] = 1;
            s[2] = 2;
            for (int i = 4; i <= n; i += 2) {
                prime[i] = false;
                s[i] = 2;
            }

            for (int i = 3; i <= n; i += 2) {
                if (prime[i]) {
                    s[i] = i;
                    for (int j = 2 * i; j <= n; j += i) {
                        prime[j] = false;
                        s[j] = i;
                    }
                }
            }

        }


        public void findAllPrime(int n, ArrayList < Node > al, int s[]) {
            int curr = s[n];
            int cnt = 1;
            while (n > 1) {
                n /= s[n];
                if (curr == s[n]) {
                    cnt++;
                    continue;

                }
                Node n1 = new Node(curr, cnt);
                al.add(n1);

                curr = s[n];
                cnt = 1;
            }
        }



        public int binarySearch(int n, int k) {
            int left = 1;
            int right = 100000000 + 5;
            int ans = 0;
            while (left <= right) {
                int mid = (left + right) / 2;
                if (n / mid >= k) {
                    left = mid + 1;
                    ans = mid;
                } else {
                    right = mid - 1;
                }
            }

            return ans;
        }
        public boolean checkPallindrom(String s) {
            char ch[] = s.toCharArray();

            for (int i = 0; i < s.length() / 2; i++) {
                if (ch[i] != ch[s.length() - 1 - i])
                    return false;
            }
            return true;
        }


        public void dfs_util(ArrayList < Integer > [] al, boolean vis[], int x, int cnt[], int sts[], int fts[], long sv[]) {

            vis[x] = true;
            long min = Long.MAX_VALUE;
            sts[cnt[0]] = x + 1;
            for (int i = 0; i < al[x].size(); i++) {

                if (!vis[al[x].get(i)]) {
                    cnt[0]++;
                    dfs_util(al, vis, al[x].get(i), cnt, sts, fts, sv);
                    if (sv[al[x].get(i)] < min && sv[al[x].get(i)] != -1) {
                        min = sv[al[x].get(i)];
                    }


                }

            }


            if (sv[x] == -1) {
                if (min == Long.MAX_VALUE) {
                    min = -1;
                }
                sv[x] = min;
            }


            return;
        }

        public void dfs(ArrayList[] al, int sts[], int fts[], long sv[]) {

            boolean vis[] = new boolean[al.length];
            int cnt[] = new int[2 * al.length + 2];
            for (int i = 0; i < al.length; i++) {
                if (!vis[i]) {

                    dfs_util(al, vis, i, cnt, sts, fts, sv);
                }
            }
        }

        public void remove(ArrayList < Integer > [] al, int x) {
            for (int i = 0; i < al.length; i++) {
                for (int j = 0; j < al[i].size(); j++) {

                    if (al[i].get(j) == x)
                        al[i].remove(j);

                }
            }
        }

        public long gcd(long a, long b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }


        public void printDivisors(long n, ArrayList <Long> al) {
            // Note that this loop runs till square root 
            for (long i = 1; i <= Math.sqrt(n); i++) {
                if (n % i == 0) {
                    // If divisors are equal, print only one 
                    if (n / i == i) {
                        al.add(i);
                    } else // Otherwise print both 
                    {
                        al.add(i);
                        al.add(n / i);
                    }

                }
            }
        }

        public static long constructSegment(long seg[], long arr[], int low, int high, int pos) {
            if (low == high) {
                seg[pos] = arr[low];
                return seg[pos];
            }
            int mid = (low + high) / 2;
            long t1 = constructSegment(seg, arr, low, mid, (2 * pos) + 1);
            long t2 = constructSegment(seg, arr, mid + 1, high, (2 * pos) + 2);
            seg[pos] = t1 + t2;
            return seg[pos];

        }
        public static long querySegment(long seg[], int low, int high, int qlow, int qhigh, int pos) {

            if (qlow <= low && qhigh >= high) {
                return seg[pos];
            } else if (qlow > high || qhigh < low) {
                return 0;
            } else {
                long ans = 0;
                int mid = (low + high) / 2;
                ans += querySegment(seg, low, mid, qlow, qhigh, (2 * pos) + 1);
                ans += querySegment(seg, mid + 1, high, qlow, qhigh, (2 * pos) + 2);
                return ans;
            }

        }
        public static int lcs(char[] X, char[] Y, int m, int n) {
            if (m == 0 || n == 0)
                return 0;
            if (X[m - 1] == Y[n - 1])
                return 1 + lcs(X, Y, m - 1, n - 1);
            else
                return Integer.max(lcs(X, Y, m, n - 1), lcs(X, Y, m - 1, n));
        }

        public static long recursion(long start, long end, long cnt[], int a, int b) {

            long min = 0;
            long count = 0;
            int ans1 = -1;
            int ans2 = -1;
            int l = 0;
            int r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] >= start) {
                    ans1 = mid;
                    r = mid - 1;
                } else {
                    l = mid + 1;
                }
            }

            l = 0;
            r = cnt.length - 1;
            while (l <= r) {
                int mid = (l + r) / 2;
                if (cnt[mid] <= end) {
                    ans2 = mid;
                    l = mid + 1;
                } else {
                    r = mid - 1;
                }
            }

            if (ans1 == -1 || ans2 == -1 || ans2 < ans1) {
                // System.out.println("min1 "+min);
                min = a;
                return a;

            } else {
                min = b * (end - start + 1) * (ans2 - ans1 + 1);
            }
            if (start == end) {
                // System.out.println("min "+min);
                return min;
            }
            long mid = (end + start) / 2;
            min = Long.min(min, recursion(start, mid, cnt, a, b) + recursion(mid + 1, end, cnt, a, b));
            // System.out.println("min "+min);
            return min;
        }

        public void dfs(int x, ArrayList < Integer > al[], boolean[] vis) {
            vis[x] = true;
            System.out.print((x + 1) + " ");
            for (int i = 0; i < al[x].size(); i++) {
                if (!vis[al[x].get(i)]) {
                    dfs(al[x].get(i), al, vis);
                }
            }
        }





        private void solve(InputReader inp, PrintWriter out1) {

            long x1 = inp.nextLong();
            long x2 = inp.nextLong();
            long a = Math.min(x1,x2);
            long b = Math.max(x1,x2);

            if(b%a==0)
            {
                out1.println(0);
                return;
            }

            long t = b-a;
            ArrayList<Long> al = new ArrayList<Long>();
            printDivisors(t, al);
            long ans=Long.MAX_VALUE;
            long k1 =-1;
            for(int i=0;i<al.size();i++)
            {
                long k = (al.get(i)-a)%al.get(i);
                while(k<0)
                {
                    k+=al.get(i);
                }
                long tem =  ((a+k)*(b+k))/al.get(i);
                if(tem<ans)
                {
                    ans=tem;
                    k1=k;
                }
            }
            

            out1.println(k1);


        }
    }





    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele implements Comparable < ele > {
    int value;
    int i;
    boolean flag;
    public ele(int value, int i) {
        this.value = value;
        this.i = i;
        this.flag = false;
    }
    public int compareTo(ele e) {
        return Integer.compare(this.value, e.value);
    }
}