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 maxn = 100000 + 100;
long long A, B;
int n;
int l, t, m;
long long sum(int i) {
  return (long long)i * A + B * ((long long)i * (i - 1) / 2);
}
bool judge(int L, int R) {
  long long remain = sum(R) - sum(L - 1);
  long long cnt = remain / m;
  if (remain % m) cnt++;
  return max(cnt, A + B * (R - 1)) <= (long long)t;
}
int main() {
  scanf("%lld %lld %d", &A, &B, &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d %d %d", &l, &t, &m);
    if (!judge(l, l)) {
      puts("-1");
      continue;
    }
    int L = l, R = 10000000;
    while (R >= L) {
      int mid = (L + R) >> 1;
      if (judge(l, mid))
        L = mid + 1;
      else
        R = mid - 1;
    }
    printf("%d\n", R);
  }
  return 0;
}
