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, B, n, t, m;
long long h(int x) { return A + (x - 1) * B; }
bool judge(long long lef, long long loc) {
  long long hl = h(loc);
  long long temp = (long long)((loc + lef) * (loc - lef + 1) / 2 * B +
                               (loc - lef + 1) * (A - B));
  long long k = min(m, loc - lef + 1);
  if (temp % k == 0)
    temp = temp / k;
  else
    temp = temp / k + 1;
  if (t >= max(h(loc), temp))
    return 1;
  else
    return 0;
}
int main() {
  scanf("%I64d%I64d%I64d", &A, &B, &n);
  for (int i = 1; i <= n; i++) {
    long long l;
    scanf("%I64d%I64d%I64d", &l, &t, &m);
    long long lef = l, rig = 3000005;
    while (lef < rig) {
      long long mid = (rig + lef + 1) / 2;
      if (judge(l, mid))
        lef = mid;
      else
        rig = mid - 1;
    }
    if (!judge(l, lef))
      printf("-1\n");
    else
      printf("%I64d\n", lef);
  }
  return 0;
}
