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 d, s;
bool vis[507][5007];
struct Node {
  int d, s;
  string str;
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ;
  cin >> d >> s;
  queue<Node> Q;
  Q.push({0, 0, ""});
  vis[0][0] = 1;
  while (!Q.empty()) {
    Node u = Q.front();
    Q.pop();
    if (u.d == 0 && u.s == s) {
      cout << u.str << "\n";
      return 0;
    }
    for (int i = (0); i <= (9); i++) {
      int a = (u.d * 10 + i) % d, b = u.s + i;
      if (vis[a][b] || b > s) continue;
      vis[a][b] = 1;
      Q.push({a, b, u.str + char(i + '0')});
    }
  }
  cout << -1 << "\n";
  return 0;
}