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
var ABn = readline().split(' ');
var A = Number(ABn[0]),
	B = Number(ABn[1]),
	n = Number(ABn[2]);

for (var i = 0; i < n; i++) {
	var line = readline().split(' ');
	var l = Number(line[0]),
		t = Number(line[1]),
		m = Number(line[2]);
	var heightAtL = A + (l - 1) * B;

	//1
	if (heightAtL > t) {
		print(-1);
		continue;
	}

	//binary search, check heightAtR and 
	var MAX = 100000000;
	var low = l, high = MAX, mid, r = -1;

	while (low <= high) {
		mid = (low + high) >> 1;
		var heightAtR = A + (mid - 1) * B;
		if (heightAtR > t) {
			high = mid - 1;
			continue;
		}
		var sum = (mid - l + 1) * heightAtL + (mid - l)* (mid - l + 1) / 2 * B;
		if (sum > t * m) {
			high = mid - 1;
			continue;
		}
		low = mid + 1;
		r = mid;
	}
	print (r);

}
