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 math import sqrt

inp = input()

l = list(map(int, inp.split(' ')))
A = l[0]
B = l[1]
n = l[2]

for i in range(n):
    inp = input()
    temp = list(map(int, inp.split(' ')))
    l = temp[0]
    t = temp[1]
    m = temp[2]

    imp = 0
    a = B/2
    b = (A - 1/2 * B)
    c = -A * (l - 1) + 3*B*l/2 - B*l*l/2 - B - t*m

    res1 = 0

    if b*b - 4 * a * c > 0:
        res1 = int((-b + sqrt(b*b - 4 * a*c) )/ (2 *a))
    else:
        imp = 1

    res2 = 0

    if (t - A - B*(-1))/B > 0:
        res2 = int((t - A - B*(-1))/B)
    else:
        imp = 1
    if res2 < l:
        imp = 1

    if not imp:
        print(min(res1, res2))
    else:
        print(-1)
