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[1000010], A, B, n, l, t, m;
long long get(int x) { return A + B * (x - 1); }
long long getnum(int x) {
  long long sum = 0;
  sum = (get(l) * (x - l + 1) + (x - l + 1) * (x - l) * 0.5 * B);
  return sum;
}
int main() {
  while (~scanf("%I64d %I64d %I64d", &A, &B, &n)) {
    for (int i = 0; i < n; i++) {
      scanf("%I64d %I64d %I64d", &l, &t, &m);
      if (get(l) > t) {
        printf("-1\n");
        continue;
      }
      long long L = l, R = (t - A) / B + 1, ans;
      while (L <= R) {
        long long mid = (L + R) / 2;
        if (getnum(mid) <= t * m) {
          ans = mid;
          L = mid + 1;
        } else
          R = mid - 1;
      }
      printf("%I64d\n", ans);
    }
  }
}
