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, n;
int main() {
  cin >> a >> b >> n;
  for (int i = 0; i < n; i++) {
    int l, t, m;
    scanf("%d %d %d", &l, &t, &m);
    if (1LL * t < 1LL * a + 1LL * (l - 1) * 1LL * b) {
      printf("-1\n");
      continue;
    }
    int l1 = l;
    int r = 3000000;
    while (l1 != r) {
      int m1 = (l1 + r + 1) / 2;
      if (1LL * a + 1LL * (m1 - 1) * b <= 1LL * t) {
        if (1LL * (1LL * a + 1LL * (l - 1) * b) * (m1 - l + 1) +
                1LL * b * (m1 - l) * (m1 - l + 1) / 2LL <=
            1LL * t * m) {
          l1 = m1;
          continue;
        }
      }
      r = m1 - 1;
    }
    printf("%d\n", l1);
  }
  return 0;
}
