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>
long long A, B, q;
int main() {
  for (scanf("%I64d%I64d%I64d", &A, &B, &q); q--;) {
    if (q == 0) q = q;
    long long l, L, t, m;
    scanf("%I64d%I64d%I64d", &L, &t, &m);
    long long r, M, res = -1;
    l = L, r = ((t) > (m) ? (t) : (m)) + l + 100;
    while (l <= r) {
      M = (l + r) / 2;
      if (A + (M - 1) * B <= t &&
          A * (M - L + 1) + ((M - 1) * M / 2 - (L - 2) * (L - 1) / 2) * B <=
              m * t)
        l = M + 1, res = ((res) > (M) ? (res) : (M));
      else
        r = M - 1;
    }
    printf("%I64d\n", res);
  }
}
