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.util.*;
import java.io.*;
import java.math.*;

public class Main {

    PrintWriter out = new PrintWriter(System.out);
    InputReader ir = new InputReader(System.in);
    final long kmod = 993960000099397l;
    

    void solve() throws IOException{
        long A = ir.readLong();
        long B = ir.readLong();
        int test = ir.readInt();
        while(test-- > 0) {
            long l = ir.readLong();
            long t = ir.readLong();
            long m = ir.readLong();
            long start = l;
            long end = 10000000l;
            long seqSumL = ((2*A + (l - 1)*B)*l)/2;
            long seqN = (A + (l - 1)*B);
         
            while(start < end) {
                long mid = (start + end + 1)/2;
                long maxH = A + (mid - 1)*B;
                long sum = ((2*A + (mid - 1)*B)*mid)/2 - seqSumL + seqN;
                if(maxH <= t && sum <= m*t) {
                    start = mid;
                   
                } else {
                    end = mid - 1;
                }
            }
            long maxH = A + (start - 1)*B;
            long sum = ((2*A + (start - 1)*B)*start)/2 - seqSumL + seqN;

            if(maxH <= t && sum <= m*t) {
                out.println(start);
            } else {
                out.println(-1);
            }
        }
    }
    
    void run() throws IOException{
        solve();
        out.close();
    }
    public static void main(String args[]) throws IOException{
        new Main().run();
    }
}
class InputReader {
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
 
    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    public final int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
    }
    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
 
    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }
        public double readDouble() {
        return Double.parseDouble(readString());
    }
 
    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}