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>
const int MOD = 1000000007;
const int MAX_N = 2e5 + 10;
const int base = 37;
using namespace std;
int A, B;
long long check1(int l, int r) {
  long long ans =
      1LL * (1LL * (A * (r - l + 1)) +
             1LL * B * (1LL * (r - 1) * (r) / 2 - 1LL * (l - 2) * (l - 1) / 2));
  return ans;
}
long long check2(int Index) {
  long long res = 1LL * (A + 1LL * B * (Index - 1));
  return res;
}
int main() {
  int q;
  scanf("%d %d %d", &A, &B, &q);
  while (q--) {
    int mn, m, t;
    scanf("%d %d %d", &mn, &t, &m);
    int l, r, mid;
    l = 0;
    r = 1e7;
    int sz = 0;
    while (l <= r) {
      mid = (l + r) >> 1;
      if (check1(mn, mid + mn - 1) <= 1LL * m * t &&
          check2(mid + mn - 1) <= t) {
        sz = mid;
        l = mid + 1;
        continue;
      }
      r = mid - 1;
    }
    if (sz)
      printf("%d\n", mn + sz - 1);
    else
      printf("-1\n");
  }
}
