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;
const int inf = (int)1e6 + 5;
int a, b, n;
int l, t, m;
long long getSum(int l, int r) {
  long long res = a * 1LL * (r - l + 1);
  res += (r * 1LL * (r - 1) * 1LL * b) / 2;
  res -= ((l - 1) * 1LL * (l - 2) * 1LL * b) / 2;
  return res;
}
bool check(int r) {
  int len = r - l + 1;
  long long lst = a + b * 1LL * (r - 1);
  if (lst > t) return false;
  if (len <= m) {
    return true;
  } else {
    long long sum = getSum(l, r);
    return sum <= t * 1LL * m;
  }
}
void solve() {
  int lft = l - 1, rht = inf;
  while (rht - lft > 1) {
    int mid = (lft + rht) / 2;
    if (check(mid))
      lft = mid;
    else
      rht = mid;
  }
  if (lft == l - 1)
    printf("-1\n");
  else
    printf("%d\n", lft);
}
int main() {
  scanf("%d%d%d", &a, &b, &n);
  for (int i = 0; i < n; i++) {
    scanf("%d%d%d", &l, &t, &m);
    solve();
  }
  return 0;
}
