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>
#pragma comment(linker, "/STACK:20000000")
using namespace std;
int ri() {
  int x;
  scanf("%d", &x);
  return x;
}
long long rll() {
  long long x;
  scanf("%lld", &x);
  return x;
}
long long mas[10000500];
void solve() {
  long long a = ri(), b = ri();
  int n = ri();
  for (int i = (int)(1); i <= (int)(10000000); i++)
    mas[i] = a + (long long)(i - 1) * b + mas[i - 1];
  for (int i = (int)(1); i <= (int)(n); i++) {
    int L = ri();
    long long t = ri(), m = ri();
    if (mas[L] - mas[L - 1] > t) {
      printf("-1\n");
      continue;
    }
    int l = L, r = 10000001;
    while (l + 1 < r) {
      int mid = (l + r) >> 1;
      long long sum = mas[mid] - mas[L - 1];
      if (sum <= t * m && mas[mid] - mas[mid - 1] <= t)
        l = mid;
      else
        r = mid;
    }
    printf("%d\n", l);
  }
}
int main() {
  solve();
  return 0;
}
