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 inp() {}
const int INF = 0x7fffffff;
long long a, b;
bool pos(long long l, long long t, long long m, long long i);
long long binser(long long l, long long t, long long m, long long lft,
                 long long rt);
long long still(long long n);
long long element(long long i);
bool pos(long long l, long long t, long long m, long long i);
int main() {
  inp();
  int n;
  long long l, t, m, r, mx, i;
  mx = 10000000LL;
  cin >> a >> b >> n;
  for (i = (0); i < (n); ++i) {
    cin >> l >> t >> m;
    if (element(l) > t) {
      cout << "-1\n";
      continue;
    }
    r = binser(l, t, m, l, mx);
    cout << r << endl;
  }
  return 0;
}
long long binser(long long l, long long t, long long m, long long lft,
                 long long rt) {
  if (lft == rt) {
    return lft;
  }
  long long md, sm, el, st;
  md = (lft + rt) / 2;
  el = element(md);
  if (el > t) {
    return binser(l, t, m, lft, md - 1);
  }
  sm = still(md) - still(l) + element(l);
  if (sm > t * m) {
    return binser(l, t, m, lft, md - 1);
  }
  if (pos(l, t, m, md + 1)) {
    return binser(l, t, m, md + 1, rt);
  }
  return md;
}
long long still(long long n) {
  long long rs, ad;
  rs = a * n;
  ad = n * (n - 1);
  ad /= 2;
  ad *= b;
  rs += ad;
  return rs;
}
long long element(long long i) {
  long long res;
  res = a + (i - 1) * b;
  return res;
}
bool pos(long long l, long long t, long long m, long long i) {
  long long sm, el, st;
  el = element(i);
  if (el > t) {
    return false;
  }
  sm = still(i) - still(l) + element(l);
  if (sm > t * m) {
    return false;
  }
  return true;
}
