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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int vis[505][5005];
struct node {
  int d, s;
  string str;
};
int d, s;
int main() {
  cin >> d >> s;
  queue<node> q;
  q.push({0, 0, ""});
  vis[0][0] = 1;
  int tries = 1e8;
  while (!q.empty() && tries--) {
    node u = q.front();
    q.pop();
    if (u.s > s) continue;
    if (u.d == 0 && u.s == s) {
      cout << u.str << endl;
      return 0;
    }
    for (int i = 0; i <= 9; ++i) {
      int fd = (u.d * 10 + i) % d;
      int fs = u.s + i;
      if (!vis[fd][fs]) {
        vis[fd][fs] = 1;
        q.push({fd, fs, u.str + (char)(i + '0')});
      }
    }
  }
  cout << "-1" << endl;
  return 0;
}