Sign Posts

Description:

Input:

The input starts with two positive integers n, k (1 ≤ n ≤ 10⁵, 1 ≤ k ≤ 5)

Next n lines contain three integers each, A_i, B_i, C_i, the coefficients of the equation that determines the road (|A_i|, |B_i|, |C_i| ≤ 10⁵, A_i² + B_i² ≠ 0).

It is guaranteed that no two roads coincide.

Output:

If there is no solution, print "NO" in the single line (without the quotes).

Otherwise, print in the first line "YES" (without the quotes).

In the second line print a single number m (m ≤ k) — the number of used signs. In the next m lines print the descriptions of their locations.

Description of a location of one sign is two integers v, u. If u and v are two distinct integers between 1 and n, we assume that sign is at the point of intersection of roads number v and u. If u =  - 1, and v is an integer between 1 and n, then the sign is on the road number v in the point not lying on any other road. In any other case the description of a sign will be assumed invalid and your answer will be considered incorrect. In case if v = u, or if v and u are the numbers of two non-intersecting roads, your answer will also be considered incorrect.

The roads are numbered starting from 1 in the order in which they follow in the input.

Sample Input:

3 1
1 0 0
0 -1 0
7 -93 0

Sample Output:

YES
1
1 2

Sample Input:

3 1
1 0 0
0 1 0
1 1 3

Sample Output:

NO

Sample Input:

2 3
3 4 5
5 6 7

Sample Output:

YES
2
1 -1
2 -1

Note:

Note that you do not have to minimize m, but it shouldn't be more than k.

In the first test all three roads intersect at point (0,0).

In the second test all three roads form a triangle and there is no way to place one sign so that it would stand on all three roads at once.