Problem: You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.

Input

The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by space.

Output

Print the required number or -1 if it doesn't exist.

Examples

Input

13 50


Output

699998


Input

61 2


Output

1000000000000000000000000000001


Input

15 50


Output

-1

Solution (in JAVA):

Solution:
//package ACM;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.List;
import java.util.Queue;
import java.util.Scanner;
import java.util.ArrayDeque;
import java.util.Collections;
public class Sove {
    public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
        TaskA solver = new TaskA();
        solver.solve(1, sc);
    }

    public static class TaskA {
        public void solve(int testNumber, Scanner sc) {
            int needMod = sc.nextInt();
            int needSum = sc.nextInt();
            int[][][] parent = new int[needSum + 1][needMod][3];
            ArrayUtils.fill(parent, -1);
            Queue<IntIntPair> q = new ArrayDeque<IntIntPair>();
            q.add(IntIntPair.makePair(0, 0));
            while (!q.isEmpty()) {
                IntIntPair cur = q.poll();
                int sum = cur.first;
                int mod = cur.second;
                for (int d = 0; d <= 9; d++) {
                    int willSum = sum + d;
                    int willMod = (mod * 10 + d) % needMod;
                    if (willSum == 0 || willSum > needSum) {
                        continue;
                    }
                    if (parent[willSum][willMod][0] == -1) {
                        parent[willSum][willMod][0] = sum;
                        parent[willSum][willMod][1] = mod;
                        parent[willSum][willMod][2] = d;
                        q.add(IntIntPair.makePair(willSum, willMod));
                    }
                }
            }
            if (parent[needSum][0][0] == -1) {
            	System.out.println(-1);
                return;
            }
            List<Integer> ans = new ArrayList<>();
            int haveSum = needSum;
            int haveMod = 0;
            while (parent[haveSum][haveMod][0] != -1) {
                int prevSum = parent[haveSum][haveMod][0];
                int prevMod = parent[haveSum][haveMod][1];
                int prevD = parent[haveSum][haveMod][2];
                ans.add(prevD);
                haveSum = prevSum;
                haveMod = prevMod;
            }
            Collections.reverse(ans);
            for (int dig : ans) {
            	System.out.print(dig);
            }
        }

    }

    public static class IntIntPair implements Comparable<IntIntPair> {
        public final int first;
        public final int second;

        public static IntIntPair makePair(int first, int second) {
            return new IntIntPair(first, second);
        }

        public IntIntPair(int first, int second) {
            this.first = first;
            this.second = second;
        }

       /* public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            IntIntPair pair = (IntIntPair) o;

            return first == pair.first && second == pair.second;
        }

        public int hashCode() {
            int result = first;
            result = 31 * result + second;
            return result;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }
*/
        public int compareTo(IntIntPair o) {
            int value = Integer.compare(first, o.first);
            if (value != 0) {
                return value;
            }
            return Integer.compare(second, o.second);
        }

    }

    public static class ArrayUtils {
        public static void fill(int[][] array, int value) {
            for (int[] row : array) {
                Arrays.fill(row, value);
            }
        }

        public static void fill(int[][][] array, int value) {
            for (int[][] subArray : array) {
                fill(subArray, value);
            }
        }

    }
/*
    public static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public int readInt() {
            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;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    public static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void print(int i) {
            writer.print(i);
        }

    }
    */
}