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>
int A, B, n;
long long bites(int l, int r, int m) {
  long long result = 0;
  long long len = r - l + 1;
  long long h1 = A + (l - 1) * (long long)B;
  long long h2 = A + (r - 1) * (long long)B;
  result = ((h1 + h2) * len) / 2;
  result = (result - 1) / m + 1;
  if (result < h2) return h2;
  return result;
}
int main() {
  int l, t, m, r, r0, r1;
  scanf("%d %d %d\n", &A, &B, &n);
  while (n--) {
    scanf("%d %d %d\n", &l, &t, &m);
    r0 = l - 1;
    r1 = l + 10000000;
    while (r0 + 1 < r1) {
      r = (r0 + r1) / 2;
      if (bites(l, r, m) <= t)
        r0 = r;
      else
        r1 = r;
    }
    if (r0 < l)
      printf("-1\n");
    else
      printf("%d\n", r0);
  }
}
