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.IOException;
import java.util.InputMismatchException;
import java.util.LinkedList;

public class Solution {
    public static void main(String[] args) {
        new Solution().solve();
        
    }
    FasterScanner in;
    //long[] sum;
    //long[] height;
    int a,b,m,t,n,l;
    public void solve()
    {
         in = new FasterScanner();
         a=in.nextInt();
         b=in.nextInt();
         n=in.nextInt();
        long some,tm,tmp,l1,r,tmp1,mid;
        loop1:
        for(int i=0;i<n;i++)
        {
            l=in.nextInt();
            t=in.nextInt();
            m=in.nextInt();
            tm=t*(long)m;
            some=a+b*(long)(l-1);
            if(some>t)
            {
                System.out.println(-1);
                continue;
            }
            long x=l+1L;
            l1=l;
            r=tm/some+l;
            while(r!=l1 && r-l1!=1)
            {
        //      System.out.println(l1+" "+r );
                mid=(l1+r)/2;
                tmp=a+(mid-1)*b;
                if(tmp>t)
                {
                    r=mid;
                    continue;
                }
                tmp1=((mid-l+1)*(long)(tmp+some))/2L;
                if(tmp1>tm)
                {
                    r=mid;
                    continue;
                }
                l1=mid;
            }
            if(r==l1)
                System.out.println(l1);
            else
            {
            //  System.out.println("l "+l1+" r "+r);
                mid=r;
                tmp=a+(mid-1)*b;
                if(tmp>t)
                {
                    
                    System.out.println(l1);
                    continue;
                }
                tmp1=((mid-l+1)*(long)(tmp+some))/2L;
                if(tmp1>tm)
                {
                    System.out.println(l1);
                    continue;
                }
            System.out.println(r);
            }
        }
    }
    
    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            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 long nextLong() {
            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 int nextInt() {
            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 int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}