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.

<image>

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;
template <class T>
T power(T a, T b) {
  T x;
  if (b == 0)
    x = 1;
  else
    x = a;
  for (size_t i = 1; i < b; i++) x *= a;
  return x;
}
long long int gcd(long long int a, long long int b) {
  return b == 0 ? a : gcd(b, a % b);
}
long long int n, m, a, b, c, ab, ba, x, y, z, avg, sum;
long long int arr2[100001], arr3[200000], arr4[200001], arr5[100001];
bool f, f1, f2;
string str, s1, s2, s3, s4;
set<int> seto;
double d, d1;
long long int x1, x2, y11, y2;
long long int mini = 100000000000000, maxi = 0;
map<int, bool> mp;
vector<long long int> v, v1, v2, v3;
int main() {
  cin >> a >> b >> n;
  for (int i = 0; i < n; i++) {
    long long int l, r, mid;
    scanf("%lld", &l);
    scanf("%lld%lld", &x, &m);
    y = l;
    r = 1 << 30;
    while (l < r) {
      mid = (l + r) / 2;
      if (l == mid) break;
      if (a * (mid - y + 1) +
                  (mid * (mid - 1) / 2 - (y - 2) * (y - 1) / 2) * b >
              x * m ||
          a + (mid - 1) * b > x) {
        r = mid;
      } else
        l = mid;
    }
    if (a * (mid - y + 1) + (mid * (mid - 1) / 2 - (y - 2) * (y - 1) / 2) * b >
            x * m ||
        a + (mid - 1) * b > x) {
      printf("-1\n");
    } else
      printf("%lld\n", mid);
  }
}
