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 *
inp=input()
a,b,c=inp.split()
a=float(a)
b=float(b)
c=float(c)
for i in range(0,int(c)):
	l,t,m=input().split()
	l=float(l)
	t=float(t)
	m=float(m)
	hl=a+(l-1.0)*b
	if hl>t:
		print (-1)
		continue
	num=(t-hl)/b+1.0
	terms=floor(num)
	num=(b-2.0*hl+sqrt((2.0*hl-b)*(2.0*hl-b)-4.0*(b)*(-2.0*t*m)))/(2.0*b)
	terms2=floor(num)
	print (int((l+min(terms,terms2)-1)))