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;
void reloc() {
  freopen("cards.in", "r", stdin);
  return;
}
int a, b, l, t, m, n;
void read() {
  scanf("%d%d%d", &a, &b, &n);
  return;
}
long long h(int pos) { return 1ll * a + 1ll * (pos - 1) * b; }
long long sum(int x1, int x2) {
  return 1ll * (2ll * a + (x1 + x2 - 2) * b) * (x2 - x1 + 1) / 2;
}
int ri, mid, le;
bool ok(int pos) {
  int len = pos - l + 1;
  long long ans = 0;
  if (h(pos) > t) return 0;
  ans = sum(l, pos);
  if (ans <= 1ll * t * m) return 1;
  return 0;
}
void work() {
  for (int i = 1; i <= n; i++) {
    scanf("%d%d%d", &l, &t, &m);
    if (t < h(l)) {
      printf("-1\n");
      continue;
    }
    ri = 1000009;
    le = l;
    while (le != ri) {
      mid = ((le + ri) >> 1) + 1;
      if (ok(mid)) {
        le = mid;
      } else
        ri = mid - 1;
    }
    printf("%d\n", le);
  }
  return;
}
int main() {
  read();
  work();
  return 0;
}
