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.

<image>

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;
long long cum[2000001], h[2000001];
long long high(long long i) { return (a + ((i - 1) * b)); }
void gen() {
  cum[1] = high(1);
  h[1] = high(1);
  for (int i = 2; i <= 2000000; i++) {
    cum[i] += (high(i) + cum[i - 1]);
    h[i] = high(i);
  }
}
bool valid(long long mid) {
  long long sum = cum[mid] - cum[l - 1];
  long long maxx = h[mid];
  return (sum <= m * t) && (maxx <= t);
}
int main() {
  while (scanf("%lld%lld%lld", &a, &b, &n) != EOF) {
    gen();
    while (n--) {
      scanf("%lld%lld%lld", &l, &t, &m);
      if (high(l) > t) {
        printf("-1\n");
        continue;
      }
      long long lo = 1, hi = 2e6, mid;
      while (lo < hi) {
        mid = (lo + hi) / 2;
        if (valid(mid))
          lo = mid;
        else
          hi = mid - 1;
        if (lo + 1 == hi) {
          if (valid(lo + 1))
            lo = hi;
          else
            hi = lo;
        }
      }
      printf("%lld\n", lo);
    }
  }
  return 0;
}
