Problem G
Skotleikur

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Recently, Elvar has been playing the new shooter that everyone is playing; Medal of Valor: Contemporary Tactics 2.

Elvar has finally played long enough to unlock access to his favourite gun, but whenever he uses it, he notices that it is not particularly good, and other players always seem to get the kill on Elvar’s target.

That’s why Elvar has been thinking how many kills and how many assists, which is when you’ve hit a target but an ally gets the kill, he has truly gotten in the time he has been using this gun.

The issue is that in MoV: CT2, you are only shown the number of points you have, where each kill grants $a$ points, and each assist grants $b$ points.

You would like to help Elvar by writing a program, which accepts the total number of points $K$ that Elvar scored in a match, the number of points each kill grants and the number of points each assist grants. The program then computes all possible combinations of kills and assists which would grant Elvar $K$ points total.

You may assume that Elvar has been using his favourite gun for the entire match.

Input

The first line of the input contains a single integer $K$, the total number of points Elvar scored in the match. The second line of the input contains a single integer $a$, the number of points each kill grants. The third and final lines of the input contains a single integer $b$, the number of points each assist grants.

Output

Output $N$, the total number of combinations of kills and asists which would grant Elvar $K$ points total. After that you should output each of the $N$ combinations. Each combination consists of two space separated integers $x_ i$, which represents the number of kills in the $i$-th combination, and $y_ i$, which represents the number of assists in the $i$-th combination, for $1 \leq i \leq N$.

The order of the combinations does not matter.

Scoring

150
100
50

2
0 3
1 1

10
10
5

2
0 2
1 0

0
100
50

1
0 0