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 = 1000000000;
const int MOD = 1000000007;
long long get(long long A, long long B, long long n, long long m) {
  long long ans = A + (n - 1) * B;
  long long s = n * (A + (A + (n - 1) * B)) / 2;
  ans = max(ans, (s + m - 1) / m);
  return ans;
}
int main() {
  long long A, B, n;
  cin >> A >> B >> n;
  while (n--) {
    long long l, t, m;
    scanf("%I64d %I64d %I64d", &l, &t, &m);
    long long low = l, high = 1000000;
    while (low < high) {
      long long mid = (low + high) / 2 + 1;
      if (get(A + (l - 1) * B, B, mid - l + 1, m) <= t)
        low = mid;
      else
        high = mid - 1;
    }
    if (get(A + (l - 1) * B, B, high - l + 1, m) > t) high = -1;
    cout << high << endl;
  }
}
