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 math
s=input()
a,b,n=s.split()
a,b,n=int(a),int(b),int(n)
for cas in range(0,n):
    s=input()
    l,t,m=s.split()
    l,t,m=int(l),int(t),int(m)
    L,R=l,(t-a)//b+1
    if R<L:
        print(-1)
        continue
    else:
        A=b
        B=2*a-b
        C=(2*a+b*l-2*b)*(1-l)-2*t*m
        ans=(-B+math.sqrt(B*B-4*A*C))/2/A
        if ans>R:
            ans=R
        print(int(ans))
        
