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
a, b, n = map(int, raw_input().split())
res = [0] * n

def parseints(s, n):
    r = [0] * n
    i = 0
    x = 0
    for c in s:
        if c == ' ':
            r[i] = x
            i += 1
            x = 0
        else:
            x = x * 10 + ord(c) - 48
    return r
# z = map(int, sys.stdin.read().split())
z = parseints(sys.stdin.read().replace('\n', ' '), 3 * n)

for i in xrange(n):
    l0, t, m = z[3 * i: 3 * i + 3]
    r = (t - a) / b + 2
    l = l0 - 1
    g = t * m + a * l + b * l * (l - 1) / 2
    while l + 1 < r:
        c = (l + r) / 2
        s = a * c + b * c * (c - 1) / 2
        if s <= g:
            l = c
        else:
            r = c

    res[i] = -1 if l < l0 else l

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