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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
        // System.out
        // .println(getElementLessOrEqualThanTAndGreaterThanL(1, 13, 3, 5));
        // System.out.println(getNWhereSumIsLessThanOrEqualToSum(1, 126, 3, 5,
        // 105));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Scanner sc = new Scanner(br);
        long constant = sc.nextLong();
        long diff = sc.nextLong();
        int queries = sc.nextInt();
        while (queries-- > 0) {
            long l = sc.nextLong();
            long t = sc.nextLong();
            long m = sc.nextLong();
            long maxsum = t * m;
            long maxElement = t;
            long n = getElementLessOrEqualThanTAndGreaterThanL(l, maxElement,
                    constant, diff);
            if (n == -1) {
                System.out.println(-1);
                continue;
            }
            n++;
            long sumOfApN = getNWhereSumIsLessThanOrEqualToSum(l, maxsum,
                    constant, diff, n);
            if (sumOfApN == -1) {
                System.out.println(-1);
                continue;
            }
            System.out.println(l + Math.min(sumOfApN, n) - 1);
        }
    }

    private static long getNWhereSumIsLessThanOrEqualToSum(long l, long sum,
            long constant, long diff, long maxNumOfElement) {
        long Tl = constant + diff * (l - 1);
        long ret = 1;
        if (sum < Tl) {
            return -1;
        }
        long min = 1;
        long max = maxNumOfElement;
        while (min <= max) {
            long temp = (min + max) / 2;
            long sumOfAp = sumOfAP(Tl, temp, diff);
            if (sumOfAp <= sum) {
                ret = temp;
                min = temp;
            } else {
                max = temp;
            }
            if ((max - min) <= 1) {
                min = min + 1;
            }
        }
        return ret;
    }

    private static long sumOfAP(long startNum, long totalCountOfElement,
            long difference) {
        long another;
        if (totalCountOfElement % 2 == 0) {
            another = (totalCountOfElement / 2)
                    * (((2 * startNum) + ((totalCountOfElement - 1) * difference)));
        } else {
            another = totalCountOfElement
                    * (startNum + (((totalCountOfElement - 1) / 2) * difference));
        }

        return another;
    }

    // private static long getNthElement(long start, long n, long diff) {
    // return start + (n - 1) * diff;
    // }

    private static long getElementLessOrEqualThanTAndGreaterThanL(long l,
            long maxElement, long constant, long diff) {
        long Tl = constant + diff * (l - 1);
        // Tl+(n-1)d<=t
        long max = maxElement - Tl;
        if (max < 0) {
            return -1;
        } else {
            return max / diff;
        }
    }
}
