Karafs is some kind of vegetable in shape of an 1 × h rectangle. Tavaspolis people love Karafs and they use Karafs in almost any kind of food. Tavas, himself, is crazy about Karafs.

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Each Karafs has a positive integer height. Tavas has an infinite 1-based sequence of Karafses. The height of the i-th Karafs is si = A + (i - 1) × B.

For a given m, let's define an m-bite operation as decreasing the height of at most m distinct not eaten Karafses by 1. Karafs is considered as eaten when its height becomes zero.

Now SaDDas asks you n queries. In each query he gives you numbers l, t and m and you should find the largest number r such that l ≤ r and sequence sl, sl + 1, ..., sr can be eaten by performing m-bite no more than t times or print -1 if there is no such number r.

Input

The first line of input contains three integers A, B and n (1 ≤ A, B ≤ 106, 1 ≤ n ≤ 105).

Next n lines contain information about queries. i-th line contains integers l, t, m (1 ≤ l, t, m ≤ 106) for i-th query.

Output

For each query, print its answer in a single line.

Examples

Input

2 1 4
1 5 3
3 3 10
7 10 2
6 4 8


Output

4
-1
8
-1


Input

1 5 2
1 5 10
2 7 4


Output

1
2
#include <bits/stdc++.h>
using namespace std;
const bool testing = false;
void program() {
  long long A, B;
  int n;
  cin >> A >> B >> n;
  for (int tc = 0; tc < n; tc++) {
    long long l, t, m;
    cin >> l >> t >> m;
    long long a = A + (l - 1) * B;
    long long b = B;
    long long r = 1;
    if (a > t)
      r = -1;
    else {
      long long v = std::max(t, m) * 2;
      while (v) {
        long long x = r + v;
        if (a * x + x * (x - 1) * b / 2 <= t * m)
          r = x;
        else
          v /= 2;
      }
      r--;
    }
    r = std::min(r, (t - a) / b);
    if (r >= 0)
      cout << r + l << endl;
    else
      cout << -1 << endl;
  }
}
int main() {
  if (!testing) {
    program();
    return 0;
  }
  FILE* fin = NULL;
  fin = fopen("in.txt", "w+");
  fprintf(fin, "2 3 1\n92947 647140 224508\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(1) => expected : \n");
  printf("215713\n");
  printf("test case(1) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "2 1 4\n1 5 3\n3 3 10\n7 10 2\n6 4 8\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(1) => expected : \n");
  printf("4\n-1\n8\n-1\n");
  printf("test case(1) => founded  : \n");
  program();
  fin = fopen("in.txt", "w+");
  fprintf(fin, "1 5 2\n1 5 10\n2 7 4\n");
  fclose(fin);
  freopen("in.txt", "r", stdin);
  printf("test case(2) => expected : \n");
  printf("1\n2\n");
  printf("test case(2) => founded  : \n");
  program();
  return 0;
}
