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
/* jslint node: true */
function Sum(a1, d, n) {
  return ((a1+a1+(n-1)*d)*n)/2;
}

var input = readline().split(" ").map(Number);
var a1, d, n;
var first = true;
var
  a1 = input[0];
  d = input[1];
  n = input[2];
while( n-- ) {
  input = readline().split(" ").map(Number);
  var
    l = input[0],
    t = input[1],
    m = input[2],
    suml = Sum(a1, d, l-1),
    tm = t*m,
    st = l,
    ed = ( ~~((t-a1)/d) ) + 1,
    md, ans;
  if( st>ed || a1+(l-1)*d>tm ) {
    ans = -1;
  } else {
    while( st<=ed ) {
      md = (st+ed)>>1;
      if( Sum(a1, d, md)-suml<=tm ) {
        ans = md;
        st = md+1;
      } else {
        ed = md-1;
      }
    }
  }
  print(ans);
}
