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
from __future__ import division
from sys import stdin


def bs():
    be, en, ans = l, 10 ** 9, -1
    while be <= en:
        md = (be + en) >> 1
        all = a * (md - l + 1) + b * (sum_n(md - 1) - sum_n(max(l - 2, 0)))
        val = max(ceil1(all, m), a + (md - 1) * b)

        if val <= t:
            be = md + 1
            ans = md
        else:
            en = md - 1

    return ans


ceil1 = lambda a, b: (a + b - 1) // b
sum_n = lambda n: (n * (n + 1)) // 2
rints = lambda: [int(x) for x in stdin.readline().split()]

a, b, n = rints()
qur, out = [rints() for _ in range(n)], []

for l, t, m in qur:
    out.append(bs())

print('\n'.join(map(str, out)))
