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>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
using namespace std;
int a, b, c, d, n, m, k;
inline bool check(int l, int r, int m, int t) {
  long long cl = (long long)(l - 1) * b + a;
  long long cr = (long long)(r - 1) * b + a;
  long long tot = (cr + cl) * (r - l + 1) / 2;
  long long c1 = (tot + m - 1) / m;
  long long c2 = cr;
  long long c = max(c1, c2);
  if (c <= t)
    return 1;
  else
    return 0;
}
int main() {
  scanf("%d%d%d", &a, &b, &n);
  for (int _n((n)-1), it(0); it <= _n; it++) {
    int sl, t, m;
    scanf("%d%d%d", &sl, &t, &m);
    if ((long long)(sl - 1) * b + a > t) {
      printf("-1\n");
      continue;
    }
    int l = sl, r = 1000001;
    while (r - l > 1) {
      int xx = (r + l) / 2;
      if (check(sl, xx, m, t))
        l = xx;
      else
        r = xx;
    }
    printf("%d\n", l);
  }
}
