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;
const int INF = (1LL << 30) - 1;
const long long int LINF = (1LL << 62) - 1;
int A, B, N, L, T, M;
int check(int R) {
  long long int num = R * 1LL * (R - 1) / 2 - (L - 1) * 1LL * (L - 2) / 2;
  long long int sum = (R - L + 1) * 1LL * A + B * 1LL * num;
  return ((A + (R - 1) * 1LL * B <= T) && (sum <= T * 1LL * M));
}
int main() {
  int lo, hi, mi, sol;
  cin.sync_with_stdio(false);
  scanf("%d%d%d", &A, &B, &N);
  while (N--) {
    scanf("%d%d%d", &L, &T, &M);
    lo = L, hi = (T - A) / B + 200;
    sol = -1;
    while (lo <= hi) {
      mi = (lo + hi) / 2;
      if (check(mi)) {
        sol = max(sol, mi);
        lo = mi + 1;
      } else
        hi = mi - 1;
    }
    printf("%d\n", sol);
  }
  return 0;
}
