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, l, t, m, s;
inline long long comb(long long first) { return (first * (first - 1LL)) / 2LL; }
inline long long h(long long i) { return A + (i - 1LL) * B; }
inline bool check(long long r) {
  long long e = comb(r) - comb(l - 1LL);
  if (B && (long double)e > 2e18 / (long double)B) return false;
  if (h(r) > t) return false;
  s = m * t;
  s -= e * B;
  s -= A * (r - l + 1LL);
  return (s >= 0LL);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> A >> B >> n;
  while (n--) {
    cin >> l >> t >> m;
    if (h(l) > t) {
      cout << -1 << '\n';
      continue;
    }
    long long lo = l, hi = max(t, m) + l + 5;
    while (lo < hi) {
      long long mid = (lo + hi) / 2LL;
      if (check(mid))
        lo = mid;
      else
        hi = mid - 1LL;
      if (lo + 1LL == hi) {
        if (check(hi))
          lo = hi;
        else
          hi = lo;
      }
    }
    cout << lo << '\n';
  }
}
