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;
const int N = 10000000;
long long num[N + 5], sum[N + 5];
int main() {
  long long A, B, l, t, m, n;
  scanf("%lld%lld%lld", &A, &B, &n);
  for (int i = 1; i <= N; i++) {
    num[i] = A + (i - 1) * B;
    sum[i] = sum[i - 1] + num[i];
  }
  long long min1 = N, min2 = N;
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld%lld", &l, &t, &m);
    if (binary_search(num + 1, num + N, t))
      min1 = lower_bound(num + 1, num + N, t) - num;
    else
      min1 = lower_bound(num + 1, num + N, t) - (num + 1);
    if (binary_search(sum + 1, sum + N, m * t + sum[l - 1]))
      min2 = lower_bound(sum + 1, sum + N, m * t + sum[l - 1]) - (sum + 1) + 1;
    else
      min2 = lower_bound(sum + 1, sum + N, m * t + sum[l - 1]) - (sum + 1);
    long long ans = min(min1, min2);
    if (ans < l)
      printf("-1\n");
    else
      printf("%lld\n", ans);
  }
  return 0;
}
