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 GCC optimize("O2")
#pragma GCC diagnostic ignored "-Wunused-variable"
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-label"
#pragma GCC diagnostic ignored "-Wsign-compare"
using namespace std;
const long long MOD = 1e+9 + 7;
const long long INFLL = 0x3f3f3f3f3f3f3f3f;
const int INF = 0x3f3f3f3f;
const long long MAXN = 1e+5 + 7;
long long a, b, t, m, lft;
bool first(long long x) {
  long long al = a - b + b * lft;
  long long ar = a - b + b * x;
  if (ar > t) return false;
  return (al + ar) * (x - lft + 1) / 2 <= m * t;
}
void solve() {
  long long n;
  cin >> a >> b >> n;
  while (n--) {
    cin >> lft >> t >> m;
    if (!first(lft)) {
      cout << -1 << '\n';
      continue;
    }
    long long l = lft, r = lft;
    while (first(r)) r *= 2;
    while (r - l > 1) {
      long long mid = (l + r) / 2;
      if (first(mid))
        l = mid;
      else
        r = mid;
    }
    cout << l << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long tc = 1;
  while (tc--) {
    long long i, j;
    solve();
  }
  return 0;
}
