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
import sys
import math


a, b, n = map(int, str.split(sys.stdin.readline()))
s = lambda i: a + (i - 1) * b
S = lambda i: a * i + b * i * (i - 1) // 2
for _ in range(n):

    l, t, m = map(int, str.split(sys.stdin.readline()))
    # Si = a * r + b * r * (r - 1) / 2
    # Si = b / 2 * r ^ 2 - (b / 2 - a) * r
    # si = a + (i - 1) * b => (si - a) / b + 1 = i

    # (S(r) - S(l-1)) / t <= m
    # S(r) <= m * t + S(l-1)
    # b / 2 * r ^ 2 - (b / 2 - a) * r - m * t - S(l-1) <= 0
    # D = (b / 2 - a) ^ 2 + 4 * b / 2 * (m * t + S(l-1))
    d = (b / 2 - a) ** 2 + 4 * b / 2 * (m * t + S(l - 1))
    if d < 0:

        print(-1)
        continue

    r = min(
        math.floor((t - a) / b + 1),
        math.floor(((b / 2 - a) + math.sqrt(d)) / b)
    )
    if r < l:

        print(-1)

    else:

        print(r)
