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
from sys import stdin

A,B,n = [int(x) for x in stdin.readline().split()]

for q in range(n):
  l,t,m = [int(x) for x in stdin.readline().split()]
  l -= 1
  if B*l+A > t:
    print(-1)
  else:
    const = A*(l)+(B*(l-1)*(l))//2
    #print(l,const)
    high = (t-A)//B+1
    low = l+1
    while high >= low:
      mid = (low+high)//2
      total = A*mid+(B*mid*(mid-1))//2-const
      if total <= t*m:
        #print(mid, total,'valid')
        low = mid+1
      else:
        #print(mid,total,'invalid')
        high = mid-1
    print(high)
