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
#!/usr/bin/env python

import math

A, B, n = map(int, raw_input().split())

ans = []

for _ in xrange(n):
	l, t, m = map(int, raw_input().split())
	
	if A + B * (l - 1) > t:
		ans.append(-1)
		continue

	r1 = (t - A) / B + 1
	D = (B-2*A)*(B-2*A)-4*B*(-2*l*A+2*A-B*(l-2)*(l-1)-2*m*t)
	r2 = int(((B-2*A) + math.sqrt(D)) / 2 / B)

	if r1 > r2:
		r1 = r2
	ans.append(r1)


print "\n".join(map(str, ans))