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

public class Karafs {

	public static void main(String[] args) throws IOException {
		skp();
		int a = nextInt();
		int b = nextInt();
		int n = nextInt();
		long[] arr = new long[2000000];
		arr[0] = a;
		for (int i = 1; i < 2000000; i++) {
			arr[i] = arr[i - 1] + a + b * (long) i;
		}

		for (int i = 0; i < n; i++) {
			skp();
			int l = nextInt() - 1;
			int t = nextInt();
			int m = nextInt();
			long sum = (long)t * m;
			int lo = l;
			int hi = l+t+20;
			int res = -1;
			int mid = 0;
			while(lo<=hi) {

				mid = lo + (hi - lo) / 2;
//				System.out.println(hi+" "+mid+" "+lo);
				long cs = arr[mid] - (l == 0 ? 0 : arr[l - 1]);
				long cx = arr[mid] - (mid == 0 ? 0 : arr[mid - 1]);
				if (cs <= sum && (arr[mid] - (mid == 0 ? 0 : arr[mid - 1])) <= t ) {
					res = mid;			
					lo = mid+1;
				} else{
					hi = mid-1;}
			}
			System.out.println(res==-1?res:res+1);
			}

		}

	

	static boolean skp() throws IOException {
		String line = r.readLine();
		if (line == null)
			return false;
		tkn = new StringTokenizer(line);
		return true;
	}

	static int nextInt() {
		return Integer.parseInt(tkn.nextToken());
	}

	static int readInt() throws NumberFormatException, IOException {
		return Integer.parseInt(r.readLine());
	}

	static long nextLong() {
		return Long.parseLong(tkn.nextToken());
	}

	static long readLong() throws NumberFormatException, IOException {
		return Long.parseLong(r.readLine());
	}

	static double nextDouble() {

		return Double.parseDouble(tkn.nextToken());
	}

	static BufferedReader r = new BufferedReader(new InputStreamReader(
			System.in));
	static StringTokenizer tkn;

}
