535_C. Tavas and Karafs
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
```python
a,b,n=map(int,input().split())
for _ in range(n):
    l,t,m=map(int,input().split())
    lo=l
    hi=100000000
    while lo<hi:
        mid=(lo+hi)//2
        count=(mid-l)+1
        first=a+(l-1)*b
        last=a+(mid-1)*b
        if last<=t and (count*(first+last))//2<=m*t:
            lo=mid+1
        else:
            hi=mid
    if mid!=lo:
        print(mid)
    else:
        count=(mid-1-l)+1
        first=a+(l-1)*b
        last=a+(mid-1-1)*b
        if last<=t and (count*(first+last))//2<=m*t and mid-1>=l:
            print(mid-1)
        else:
            print(-1)
```