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
def seq_sum(A,r,l,B):
    return A*(r-l+1)+B*((r*(r-1))/2 - (((l-1)*(l-2))/2))


def read():
    return map(int, raw_input().strip().split(' '))


A,B,n = read()
for i in xrange(n):
    l,t,m=read()



    r = (t-A)/B + 1
    q = 9*B**2+4*l**2*B**2-12*l*B**2-12*B*A+8*l*B*A+8*t*m*B+4*A**2
    r = min(r, int( ( (-2*A+B) + (q**0.5) ) / (2 * B) ))

    s_r = A+B*(r-1)
    if s_r<=t and seq_sum(A,r,l,B)>0:
        print r
    else:
        print -1
