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;
long long A, B, n;
long long cal(int x) { return A * x + B * (x - 1) * x / 2; }
long long find(long long x) {
  int l = 1;
  int r = 1000001;
  int mid = (l + r) / 2;
  while (l < r) {
    if (cal(mid) <= x)
      l = mid + 1;
    else
      r = mid;
    mid = (l + r) / 2;
  }
  return l - 1;
}
int main() {
  scanf("%I64d %I64d %I64d", &A, &B, &n);
  while (n--) {
    long long l, t, m, r1, r2, w3;
    scanf("%I64d %I64d %I64d", &l, &t, &m);
    w3 = A + (l - 1) * B;
    if (t < w3)
      printf("-1\n");
    else {
      r1 = (t - A) / B + 1;
      r2 = find(t * m + cal(l - 1));
      printf("%I64d\n", r1 < r2 ? r1 : r2);
    }
  }
  return 0;
}
