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, l, t, m, r;
long long S(long long i) { return A + ((i - 1) * B); }
long long Z(long long p, long long q) {
  return ((q - p + 1) * (S(p) + S(q))) / 2;
}
int main() {
  scanf("%ld %ld %ld\n", &A, &B, &n);
  while (n--) {
    scanf("%ld %ld %ld\n", &l, &t, &m);
    if (S(l) > t) {
      printf("-1\n");
      continue;
    }
    long long lo = l, la = 10e7;
    while (lo < la) {
      long long mid = (lo + la) / 2;
      if (S(mid) <= t && Z(l, mid) <= m * t) {
        lo = mid + 1;
      } else {
        la = mid;
      }
    }
    printf("%ld\n", lo - 1);
  }
  return 0;
}
