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;
int n;
bool check(int l, int mid, int t, int m) {
  int r = l + mid - 1;
  int len = r - l + 1;
  long long sum = (long long)A * len + (long long)(l - 1 + r - 1) * len * B / 2;
  return max((sum + m - 1) / m, A + (long long)(r - 1) * B) <= t;
}
int main() {
  cin >> A >> B >> n;
  for (int q = 0; q < n; ++q) {
    int l, t, m;
    scanf("%d %d %d", &l, &t, &m);
    int a = 0, b = 0x3F3F3F3F;
    while (a <= b) {
      int mid = (a + b) >> 1;
      if (!check(l, mid, t, m)) {
        b = mid - 1;
      } else {
        a = mid + 1;
      }
    }
    if (a >= 2 && check(l, a - 1, t, m)) {
      printf("%d\n", l + a - 2);
    } else {
      printf("-1\n");
    }
  }
}
