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 = 1e9, mod = 1e9 + 7, N = 3e5;
const long long linf = 1e18;
long long a, b, q;
long long sum(long long l, long long r) {
  return ((r - l + 1) * (a + (l - 1) * b + a + (r - 1) * b)) / 2;
}
int main() {
  scanf("%I64d%I64d%I64d", &a, &b, &q);
  for (int p = 0; p < q; p++) {
    long long l, t, m;
    scanf("%I64d%I64d%I64d", &l, &t, &m);
    long long L = l, R = 1e12;
    long long ans = -1;
    while (L <= R) {
      long long md = (L + R) >> 1;
      if (a + (md - 1) * b <= t && sum(l, md) <= t * m) {
        ans = md;
        L = md + 1;
      } else
        R = md - 1;
    }
    printf("%I64d\n", ans);
  }
  return 0;
}
