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 SUM[1000005];
int binarySearch(int left, int right, long long x) {
  int middle = (left + right) / 2;
  if (left == right) {
    if (SUM[left] > x) return -1;
    return left;
  }
  if (left + 1 == right) {
    if (SUM[right] <= x) return right;
    return left;
  }
  if (SUM[middle] <= x)
    return binarySearch(middle, right, x);
  else
    return binarySearch(left, middle - 1, x);
}
int main() {
  int A, B, N;
  cin >> A >> B >> N;
  SUM[0] = 0;
  for (int i = 1; i < 1000005; i++) {
    long long x = A + (long long)B * (i - 1);
    SUM[i] = (long long)SUM[i - 1] + x;
  }
  for (int i = 1; i <= N; i++) {
    int L, R, T, M;
    cin >> L >> T >> M;
    R = (T - A) / B + 1;
    if (R < L)
      cout << "-1\n";
    else
      cout << binarySearch(L, R, (long long)T * M + SUM[L - 1]) << "\n";
  }
}
