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 MAXN = 1e5 + 10;
long long A, B;
bool check(long long L, long long R, long long m, long long t) {
  long long sum = (R - L + 1) * A + (L + R - 2) * (R - L + 1) / 2 * B;
  if (sum <= m * t && A + B * (R - 1) <= t) return true;
  return false;
}
int main() {
  int n;
  while (scanf("%d%I64d%I64d", &A, &B, &n) != EOF) {
    for (int i = 0; i < n; ++i) {
      long long l, t, m;
      scanf("%I64d%I64d%I64d", &l, &t, &m);
      int L = l, R = l + t, ans = -1;
      while (L <= R) {
        int mid = (L + R) >> 1;
        if (check(l, mid, m, t))
          ans = mid, L = mid + 1;
        else
          R = mid - 1;
      }
      printf("%d\n", ans);
    }
  }
  return 0;
}
