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 l, A, B, lh, mid, now, L, R, m, t, All, xx;
int n, i;
bool Get(long long x, long long y) {
  long long r = (y - 1) * B + A, ans;
  ans = (lh + r) * (y - x + 1) / 2;
  if (ans <= All)
    return 1;
  else
    return 0;
}
int main() {
  xx = 1000000;
  scanf("%lld%lld%d", &A, &B, &n);
  for (i = 1; i <= n; i++) {
    scanf("%lld%lld%lld", &l, &t, &m);
    lh = (l - 1) * B + A;
    if (lh > t) {
      printf("-1\n");
      continue;
    }
    L = l;
    R = xx * xx + 1;
    while (R - L > 1) {
      mid = (L + R) / 2;
      now = (mid - 1) * B + A;
      if (now <= t)
        L = mid;
      else
        R = mid;
    }
    R = L;
    L = l;
    All = m * t;
    if (Get(L, R)) {
      printf("%lld\n", R);
      continue;
    }
    while (R - L > 1) {
      mid = (R + L) / 2;
      if (Get(l, mid))
        L = mid;
      else
        R = mid;
    }
    printf("%lld\n", L);
  }
  return 0;
}
