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
input = sys.stdin.readline

a, b, n, l, t, m = -1, -1, -1, -1, -1, -1

def is_valid(mid):
    biggest = a + (mid - 1) * b;
    if t < biggest: 
        return False
    sum = ((mid - l + 1) * (a + (l - 1) * b + biggest)) // 2
    return t >= biggest and m * t >= sum

def binary_search(b, e):
    while b <= e:
        mid = b + e >> 1
        if is_valid(mid):
            b = mid + 1
        else:
            e = mid - 1
    return b - 1

a, b, n = map(int, input().split())
for _ in range(n):
    l, t, m = map(int, input().split())
    res = binary_search(l, l + int(1e6))
    print(-1 if res == l - 1 else res)
