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
# -*- coding: utf-8 -*-
"""
Created on Wed Apr 15 01:59:52 2015

codeforces 299 Div 2 C
"""
import sys


def read_data():
    A, B, n = map(int, input().split())
    ltm = sys.stdin.readlines()
    return A, B, ltm


def solve(A, B, ltm):
    for line in ltm:
        L, t, m = map(int, line.split())
        print(max_r(L, t, m, A, B))

memo = dict()
def max_r(L, t, m, A, B):
    global memo
    if (L, t, m) in memo:
        return memo[L, t, m]
    r_upper = (t - A) // B + 2
    if r_upper <= L:
        memo[L, t, m] = -1
        return -1
    r_lower = L
    threshold = t * m
    while r_upper > r_lower + 1:
        mid = (r_upper + r_lower) // 2
        if (2 * A + B * (L + mid - 2)) * (mid - L + 1) // 2 <= threshold:
            r_lower = mid
        else:
            r_upper = mid
    memo[L, t, m] = r_lower
    return r_lower


A, B, ltm = read_data()
solve(A, B, ltm)
