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
a,b,n=[int(x) for x in input().split()]
ltm=[[]]*n
for i in range(n):
    ltm[i]=[int(x) for x in input().split()]
for i in range(n):
    l,t,m=ltm[i]
    maxr=(t-a)//b+1
    minr=l
    while maxr>=minr:
        r=(maxr+minr)//2
        if t*m>=(r-l+1)*(2*a+b*(r+l-2))/2:
            minr=r+1
        else:
            maxr=r-1
    r=maxr
    if r<l:
        print(-1)
    else:
        print(r)