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>
const int MOD = 1000000007;
using namespace std;
long long A, B;
bool isOk(long long l, long long r, long long t, long long m) {
  long long tot = (r + 1) * A + ((r * (r + 1)) / 2) * B;
  l--;
  tot -= (l + 1) * A + ((l * (l + 1)) / 2) * B;
  return r * B + A <= t && tot <= t * m;
}
int main() {
  scanf("%lld", &(A));
  scanf("%lld", &(B));
  long long n;
  scanf("%lld", &(n));
  ;
  for (int k = (0); k < (n); k++) {
    long long l;
    scanf("%lld", &(l));
    ;
    long long t;
    scanf("%lld", &(t));
    ;
    long long m;
    scanf("%lld", &(m));
    ;
    l--;
    long long lo = l;
    long long hi = (long long)1e9;
    while (lo < hi) {
      long long mid = (lo + hi + 1) / 2;
      if (isOk(l, mid, t, m)) {
        lo = mid;
      } else {
        hi = mid - 1;
      }
    }
    printf("%lld\n", isOk(l, lo, t, m) ? (lo + 1) : (-1));
  }
}
