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;
int A, B;
long long GetSum(int L, int R) {
  long long a = (L - 1) * B + A;
  long long n = R - L + 1;
  return n * a + n * (n - 1) / 2 * B;
}
int query(int F, int t, int m) {
  long long a = 1LL * (F - 1) * B + A;
  if (a > t) return -1;
  int L = F, R = (t - A) / B + 1;
  while (L < R) {
    int Mid = (L + R + 1) / 2;
    if (GetSum(F, Mid) <= 1LL * t * m)
      L = Mid;
    else
      R = Mid - 1;
  }
  return L;
}
int main() {
  scanf("%d%d", &A, &B);
  int ops;
  scanf("%d", &ops);
  for (int i = 1; i <= ops; i++) {
    int F, t, m;
    scanf("%d%d%d", &F, &t, &m);
    printf("%d\n", query(F, t, m));
  }
  return 0;
}
