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>
int A, B, q, L, t, m;
long long f(int i) { return A + (i - 1LL) * B; }
long long sum(int n) { return 1LL * A * n + (n - 1LL) * n / 2 * B; }
int main() {
  scanf("%d%d%d", &A, &B, &q);
  while (q--) {
    scanf("%d%d%d", &L, &t, &m);
    int l = L - 1, r = (int)1e6 + 5;
    while (r - l > 1) {
      int mid = l + r >> 1;
      if (f(mid) <= t && sum(mid) - sum(L - 1) <= 1LL * t * m)
        l = mid;
      else
        r = mid;
    }
    if (l == L - 1)
      puts("-1");
    else
      printf("%d\n", l);
  }
}
