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>
long long a, b, n, l, t, m;
long long getv(long long p) { return a + (p - 1) * b; }
long long getsum(long long mid) { return mid * a + mid * (mid - 1) / 2 * b; }
int main() {
  scanf("%lld%lld%lld", &a, &b, &n);
  while (n--) {
    scanf("%lld%lld%lld", &l, &t, &m);
    if (getv(l) > t)
      puts("-1");
    else {
      long long le = l, ri = 1e7, mid;
      while (le <= ri) {
        mid = le + (ri - le) / 2;
        if ((getsum(mid) - getsum(l - 1) <= t * m) && (a + (mid - 1) * b <= t))
          le = mid + 1;
        else
          ri = mid - 1;
      }
      printf("%lld\n", le - 1);
    }
  }
  return 0;
}
